##
## Attaching package: 'Matrix'
## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpack
All data were used in the factorAnalysis1.1.html document you already received.
A series of factoro analyses were run on all items in the file factorAnalysis1.1.html. THe literature suggests doing this so you can compare both statistical measures of how well it fits, and also how logical the grouping of factors is according to knowledge of the subject.
This set of analyses showed that some items had really low communalities, meaning that they didn’t covary much with any of the other items. This means they will not be robust parts of any factor, and they recommend that you remove these from the analysis.
Models with different numbers of factors had different numbers of items with communalities less than 0.4. So a new data set was made for each number of factors, with only the items with communalities of 0.4 or larger.
Similarly, the loading represents the amount of variation in an item due to the factor in which it is classified. Several items had low loadings (most of these items also had low communalities). We removed items with loadings less than 0.32.
Because each number of factors require a different data set (different numbers of items), all the steps had to be rerun sstarting with imputation. Those are the models included in this document.
Testing analyses from 12 - 18 factors.
include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.
Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (201 0)
This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.
## Warning in polychoric(ddNum12, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 916 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.
The chi-squared for the Bartlett test is 3.3855482^{4} with 1035 DF, p = 0e+00.
From EFAtools::KMO documentation:
The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis
The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.
## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.
[1] 0.8510849
## Warning in polychoric(imputedNumericDF12, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 916 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.
The chi-squared for the Bartlett test is 3.2708769^{4} with 1035 DF, p = 0e+00.
From EFAtools::KMO documentation:
The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis
The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.
## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.
[1] 0.8510849
For factor analysis, it is recommended that some of the item
correlationsshould be between 0.3 and 0.9. Polychoric correlations were
computed using the polychoric function in the
psych package in R with options smooth = TRUE
to adjust for non-positive-definite matrices and
correct = 0.01 to avoid computation problems with
covariance of zero.
The minimum correlation in this data set is -0.477. The maximum correlation in this data set is 0.856.
#### Post-Imputation
The post imputation polyserial correlation was also computed using
the polychoric function, with no setting
smooth = TRUE and correct = 0.01.
The minimum correlation was -0.467. The maximum correlation was 0.851.
From the EFAtools documentation:
Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.
Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not
PCA) - fm = “wls” (weighted least squares because pa gave errors and
weighted recommended for ordinal data. - use = “all.obs” (since we have
imputed missing values, we can use all data points) - cor = “poly” (use
polychoric correlation matrix) - n.iter = 100 (run for 100
iterations)
The suggested number of factors is 11.
MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.
| Number of Factors | MAP value |
|---|---|
| 1 | 0.0339 |
| 2 | 0.0297 |
| 3 | 0.0230 |
| 4 | 0.0200 |
| 5 | 0.0181 |
| 6 | 0.0174 |
| 7 | 0.0164 |
| 8 | 0.0158 |
| 9 | 0.0140 |
| 10 | 0.0141 |
| 11 | 0.0142 |
| 12 | 0.0148 |
| 13 | 0.0156 |
| 14 | 0.0165 |
| 15 | 0.0176 |
| 16 | 0.0188 |
| 17 | 0.0204 |
| 18 | 0.0214 |
## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 916 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.
Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.7639861. Should be > 0.9; need reference)
| fanal12.communality | |
|---|---|
| TRAIN01 | 0.46 |
| TRAIN03 | 0.43 |
| TRAIN04 | 0.59 |
| TRAIN07 | 0.62 |
| AGG09 | 0.78 |
| AGG10 | 0.67 |
| AGG14 | 0.48 |
| AGG15 | 0.76 |
| AGG16 | 0.76 |
| AGG18 | 0.72 |
| AGG19 | 0.73 |
| AGG20 | 0.52 |
| FEAR21 | 0.83 |
| FEAR23 | 0.80 |
| FEAR24 | 0.86 |
| FEAR25 | 0.42 |
| FEAR26 | 0.42 |
| FEAR27 | 0.81 |
| FEAR28 | 0.66 |
| FEAR30 | 0.35 |
| FEAR31 | 0.71 |
| SEPR32 | 0.68 |
| SEPR33 | 0.66 |
| SEPR34 | 0.65 |
| EXCITE35 | 0.46 |
| EXCITE36 | 0.57 |
| EXCITE37 | 0.64 |
| EXCITE38 | 0.64 |
| PLAY43 | 0.55 |
| PLAY44 | 0.82 |
| PLAY45 | 0.77 |
| PLAY46 | 0.72 |
| IMP47 | 0.58 |
| IMP48 | 0.47 |
| MISC52 | 0.56 |
| MISC53 | 0.51 |
| MISC54 | 0.65 |
| MISC55 | 0.68 |
| MISC56 | 0.62 |
| MISC59 | 0.61 |
| MISC61 | 0.47 |
| MISC62 | 0.43 |
| MISC64 | 0.60 |
| MISC65 | 0.65 |
| MISC66 | 0.69 |
| MISC67 | 0.59 |
There are 1 items with communality < 0.40.
| fanal12.communality | item | |
|---|---|---|
| FEAR30 | 0.35 | FEAR30 |
| PA1 | PA3 | PA11 | PA2 | PA7 | PA6 | PA5 | PA8 | PA4 | PA10 | PA12 | PA9 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| TRAIN01 | -0.09 | 0.12 | 0.05 | -0.04 | -0.08 | -0.05 | 0.03 | 0.00 | -0.01 | 0.59 | 0.02 | 0.06 |
| TRAIN03 | -0.02 | -0.03 | 0.00 | -0.02 | 0.03 | 0.08 | 0.11 | -0.04 | 0.03 | 0.61 | 0.03 | 0.02 |
| TRAIN04 | 0.04 | 0.20 | -0.02 | -0.05 | -0.01 | 0.02 | 0.02 | 0.01 | -0.07 | 0.63 | 0.11 | -0.05 |
| TRAIN07 | 0.06 | 0.60 | -0.08 | -0.06 | -0.05 | 0.00 | 0.02 | 0.01 | -0.01 | 0.30 | -0.02 | -0.02 |
| AGG09 | 0.19 | 0.03 | 0.77 | 0.03 | 0.08 | -0.03 | -0.05 | 0.00 | -0.03 | 0.05 | 0.08 | -0.10 |
| AGG10 | -0.03 | -0.02 | 0.80 | 0.09 | -0.02 | -0.01 | 0.12 | 0.01 | 0.06 | -0.03 | -0.06 | 0.06 |
| AGG14 | 0.00 | 0.08 | 0.66 | 0.02 | -0.01 | 0.05 | 0.11 | 0.01 | 0.02 | -0.05 | -0.05 | 0.11 |
| AGG15 | 0.27 | 0.01 | 0.73 | -0.03 | 0.02 | -0.01 | -0.04 | -0.11 | 0.12 | 0.00 | 0.01 | 0.06 |
| AGG16 | -0.19 | 0.05 | 0.34 | -0.06 | 0.05 | 0.01 | -0.05 | 0.37 | 0.43 | 0.06 | 0.00 | -0.18 |
| AGG18 | -0.20 | 0.01 | 0.32 | -0.02 | -0.03 | -0.05 | -0.03 | 0.34 | 0.47 | 0.03 | 0.10 | -0.14 |
| AGG19 | 0.02 | 0.04 | 0.05 | 0.05 | -0.01 | 0.09 | 0.02 | 0.01 | 0.80 | -0.01 | -0.02 | -0.07 |
| AGG20 | 0.05 | -0.04 | -0.07 | -0.07 | 0.03 | -0.03 | 0.01 | -0.07 | 0.74 | -0.02 | 0.09 | 0.13 |
| FEAR21 | 0.81 | 0.00 | 0.14 | -0.03 | 0.02 | 0.01 | 0.00 | 0.09 | 0.01 | 0.00 | 0.04 | -0.03 |
| FEAR23 | 0.70 | 0.00 | 0.20 | -0.06 | 0.04 | 0.00 | 0.05 | 0.17 | -0.06 | -0.03 | 0.06 | -0.12 |
| FEAR24 | 0.79 | 0.02 | 0.16 | -0.12 | -0.04 | 0.06 | -0.02 | 0.16 | -0.02 | -0.05 | 0.02 | -0.04 |
| FEAR25 | 0.32 | 0.17 | -0.07 | 0.03 | 0.29 | 0.03 | 0.04 | 0.09 | 0.06 | 0.12 | -0.01 | 0.03 |
| FEAR26 | 0.53 | 0.03 | -0.03 | 0.12 | 0.01 | -0.05 | 0.10 | 0.06 | 0.24 | 0.04 | -0.05 | 0.20 |
| FEAR27 | 0.15 | 0.00 | -0.03 | 0.01 | 0.02 | -0.01 | 0.02 | 0.84 | 0.03 | -0.02 | 0.00 | 0.03 |
| FEAR28 | 0.55 | 0.11 | -0.11 | 0.08 | 0.38 | 0.03 | 0.05 | 0.05 | 0.08 | 0.05 | -0.04 | -0.03 |
| FEAR30 | 0.25 | 0.06 | -0.11 | 0.10 | 0.17 | -0.06 | 0.15 | 0.03 | 0.29 | 0.06 | -0.06 | 0.28 |
| FEAR31 | 0.12 | 0.02 | -0.11 | 0.01 | 0.06 | 0.00 | 0.04 | 0.80 | -0.04 | 0.02 | -0.01 | 0.08 |
| SEPR32 | 0.09 | 0.00 | 0.00 | -0.07 | -0.04 | 0.07 | 0.78 | 0.00 | 0.06 | -0.06 | 0.04 | -0.07 |
| SEPR33 | -0.06 | 0.02 | 0.00 | 0.02 | 0.02 | 0.00 | 0.81 | 0.05 | -0.03 | 0.04 | -0.01 | 0.02 |
| SEPR34 | -0.06 | -0.01 | 0.07 | -0.01 | 0.05 | -0.03 | 0.78 | 0.01 | -0.05 | 0.07 | 0.04 | 0.03 |
| EXCITE35 | 0.08 | 0.07 | 0.00 | -0.09 | -0.11 | 0.63 | 0.14 | 0.01 | -0.01 | -0.03 | 0.03 | -0.01 |
| EXCITE36 | 0.05 | 0.05 | -0.02 | 0.18 | 0.02 | 0.67 | -0.04 | -0.08 | 0.01 | -0.04 | 0.04 | -0.01 |
| EXCITE37 | -0.03 | 0.00 | 0.03 | -0.07 | 0.00 | 0.82 | 0.01 | 0.02 | 0.00 | 0.02 | -0.01 | 0.01 |
| EXCITE38 | -0.01 | -0.12 | -0.04 | 0.05 | 0.08 | 0.76 | -0.03 | 0.02 | 0.03 | 0.06 | 0.00 | 0.05 |
| PLAY43 | -0.26 | 0.02 | -0.26 | 0.53 | 0.00 | 0.08 | -0.04 | 0.08 | -0.06 | -0.07 | 0.02 | 0.05 |
| PLAY44 | 0.02 | 0.01 | -0.03 | 0.86 | -0.03 | 0.04 | -0.02 | 0.00 | 0.10 | 0.01 | 0.04 | -0.08 |
| PLAY45 | 0.00 | 0.01 | 0.06 | 0.83 | -0.05 | 0.00 | -0.05 | 0.07 | -0.09 | -0.12 | 0.06 | 0.00 |
| PLAY46 | -0.02 | -0.15 | 0.14 | 0.79 | 0.01 | 0.02 | 0.04 | -0.08 | -0.02 | 0.07 | -0.02 | -0.02 |
| IMP47 | 0.02 | -0.10 | 0.01 | 0.12 | 0.02 | 0.08 | -0.04 | 0.06 | 0.00 | 0.24 | 0.60 | 0.12 |
| IMP48 | -0.01 | -0.01 | 0.00 | 0.06 | 0.05 | 0.09 | 0.03 | 0.05 | 0.06 | 0.13 | 0.51 | 0.15 |
| MISC52 | -0.07 | 0.09 | 0.15 | -0.09 | 0.01 | 0.07 | -0.04 | 0.12 | -0.05 | -0.04 | 0.03 | 0.69 |
| MISC53 | -0.08 | -0.02 | 0.03 | -0.10 | -0.04 | 0.02 | 0.03 | 0.02 | 0.04 | 0.09 | 0.15 | 0.62 |
| MISC54 | 0.02 | 0.14 | -0.01 | -0.04 | 0.72 | 0.06 | -0.02 | 0.02 | 0.02 | 0.02 | -0.05 | 0.08 |
| MISC55 | -0.03 | -0.05 | 0.03 | 0.03 | 0.84 | 0.01 | 0.07 | 0.00 | 0.02 | -0.01 | -0.05 | -0.07 |
| MISC56 | -0.08 | 0.00 | 0.05 | -0.08 | 0.79 | -0.02 | -0.03 | 0.03 | -0.04 | -0.04 | 0.13 | 0.01 |
| MISC59 | 0.06 | 0.12 | -0.10 | 0.07 | 0.01 | 0.00 | 0.27 | -0.10 | 0.08 | -0.06 | 0.60 | 0.01 |
| MISC61 | -0.03 | 0.09 | 0.06 | 0.27 | -0.10 | 0.23 | 0.16 | -0.11 | -0.05 | -0.16 | 0.31 | -0.15 |
| MISC62 | -0.14 | 0.42 | 0.07 | -0.02 | -0.02 | 0.07 | -0.02 | 0.31 | 0.11 | 0.01 | 0.13 | -0.03 |
| MISC64 | -0.10 | 0.78 | 0.06 | 0.00 | 0.00 | -0.02 | 0.03 | -0.04 | -0.01 | 0.00 | -0.04 | 0.02 |
| MISC65 | -0.09 | 0.72 | 0.03 | -0.02 | -0.01 | -0.01 | 0.02 | 0.05 | 0.05 | 0.11 | 0.02 | 0.07 |
| MISC66 | 0.23 | 0.59 | -0.01 | -0.05 | 0.20 | -0.05 | 0.03 | -0.02 | -0.04 | 0.08 | 0.05 | 0.01 |
| MISC67 | 0.18 | 0.58 | 0.01 | -0.12 | 0.16 | -0.02 | 0.03 | 0.02 | -0.01 | -0.07 | 0.09 | 0.00 |
| largest | maximum | itemNames | itemDescriptions | |
|---|---|---|---|---|
| 13 | PA1 | 0.81 | FEAR21 | When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel |
| 14 | PA1 | 0.70 | FEAR23 | When an unfamiliar person visits your home or approaches the dog when in his/her home kennel |
| 15 | PA1 | 0.79 | FEAR24 | When an unfamiliar person tries to touch or pet the dog |
| 16 | PA1 | 0.32 | FEAR25 | In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc. |
| 17 | PA1 | 0.53 | FEAR26 | When examined/treated by a veterinarian |
| 19 | PA1 | 0.55 | FEAR28 | When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.) |
| 43 | PA10 | 0.59 | TRAIN01 | Is hard to recall when off the leash |
| 44 | PA10 | 0.61 | TRAIN03 | Is slow to obey a ‘stay’ command |
| 45 | PA10 | 0.63 | TRAIN04 | Has difficulty attending/listening to things you say or do |
| 1 | PA11 | 0.77 | AGG09 | Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash |
| 2 | PA11 | 0.80 | AGG10 | Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel |
| 3 | PA11 | 0.66 | AGG14 | When strangers walk past when the dog is in his/her home run or kennel |
| 4 | PA11 | 0.73 | AGG15 | When an unfamiliar person tries to touch or pet the dog |
| 22 | PA12 | 0.60 | IMP47 | Impulsive; doesn’t seem to think before s/he acts |
| 23 | PA12 | 0.51 | IMP48 | Becomes frustrated/impatient in a wide range of situations |
| 29 | PA12 | 0.60 | MISC59 | Hyperactive, restless, has trouble settling down |
| 30 | PA12 | 0.31 | MISC61 | Active, energetic, always on the go |
| 36 | PA2 | 0.53 | PLAY43 | Eagerly engages in play with new/unfamiliar people |
| 37 | PA2 | 0.86 | PLAY44 | Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person |
| 38 | PA2 | 0.83 | PLAY45 | Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown |
| 39 | PA2 | 0.79 | PLAY46 | Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task |
| 31 | PA3 | 0.42 | MISC62 | Becomes highly excited and/or distracted when encountering unfamiliar dogs |
| 32 | PA3 | 0.78 | MISC64 | When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects |
| 33 | PA3 | 0.72 | MISC65 | Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.) |
| 34 | PA3 | 0.59 | MISC66 | Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work |
| 35 | PA3 | 0.58 | MISC67 | Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work |
| 46 | PA3 | 0.60 | TRAIN07 | Unfocused; is easily distracted by interesting sights, sounds or smells |
| 5 | PA4 | 0.43 | AGG16 | When approached directly by an unfamiliar dog while being walked/exercised on a leash |
| 6 | PA4 | 0.47 | AGG18 | When barked, growled, or lunged at by another dog |
| 7 | PA4 | 0.80 | AGG19 | Towards other familiar dogs |
| 8 | PA4 | 0.74 | AGG20 | When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog |
| 20 | PA4 | 0.29 | FEAR30 | When groomed or bathed |
| 40 | PA5 | 0.78 | SEPR32 | Restlessness/agitation/pacing when left alone |
| 41 | PA5 | 0.81 | SEPR33 | Barking or whining when left alone |
| 42 | PA5 | 0.78 | SEPR34 | Chewing/scratching at doors, floor, fencing, etc., when left alone |
| 9 | PA6 | 0.63 | EXCITE35 | Excitable when you first arrive home, or at the dog’s kennel, after a brief absence |
| 10 | PA6 | 0.67 | EXCITE36 | Excitable when playing with you or other familiar persons |
| 11 | PA6 | 0.82 | EXCITE37 | Excitable just before being taken out for a walk |
| 12 | PA6 | 0.76 | EXCITE38 | Excitable just before being taken out for work or training |
| 26 | PA7 | 0.72 | MISC54 | Reluctant to/nervous about crossing grates or other unfamiliar surfaces |
| 27 | PA7 | 0.84 | MISC55 | Reluctant to/nervous about crossing shiny or slippery floors |
| 28 | PA7 | 0.79 | MISC56 | Nervous or frightened when ascending or descending some types of stairs |
| 18 | PA8 | 0.84 | FEAR27 | When approached directly by an unfamiliar dog |
| 21 | PA8 | 0.80 | FEAR31 | When barked, growled, or lunged at by an unfamiliar dog |
| 24 | PA9 | 0.69 | MISC52 | Begs persistently for food when people are eating |
| 25 | PA9 | 0.62 | MISC53 | Steals food |
| PA1 | PA3 | PA11 | PA2 | PA7 | PA6 | PA5 | PA8 | PA4 | PA10 | PA12 | PA9 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| alpha | 0.797 | 0.787 | 0.76 | 0.812 | 0.718 | 0.787 | 0.735 | 0.803 | 0.715 | 0.652 | 0.661 | 0.623 |
omega is thought to be better measure of reliability than alpha, because it looks at the relationships between all the items rather than just the ones within each factor. It’s different than alpha because it assumes that there is a genral factor, g, that all items have in common. This is listed as the first row of the table below.
There are three omegas for each factor:
From EFAtools::OMEGA documentation:
Omegas refer to the correlation between a factor and a unit-weighted composite score and thus the true score variance in a unit-weighted composite based on the respective indicators. Omega total is the total true score variance in a composite. Omega hierarchical is the true score variance in a composite that is attributable to the general factor, and omega subscale is the true score variance in a composite attributable to all subscales / group factors (for the whole scale) or to the specific subscale / group factor (for subscale composites).
Interpretation of omega_subscale
no universal guideline
0.50 is minimum, 0.75 preferable (watkins books,rodrigues16, zimbarg2005
## Omega total, omega hierarchical, omega subscale, H index, explained common variance (ECV), and percent of uncontaminated correlations (PUC) for the general factor (top row) and omegas and H index for the group factors:
##
## tot hier sub H ECV PUC
## g 0.943 0.548 0.215 0.875 0.24 0.929
## F1 0.818 0.314 0.504 0.786
## F2 0.640 0.159 0.482 0.575
## F3 0.824 0.132 0.691 0.806
## F4 0.514 0.091 0.422 0.575
## F5 0.825 0.069 0.756 0.860
## F6 0.830 0.407 0.424 0.688
## F7 0.654 0.181 0.473 0.717
## F8 0.844 0.147 0.697 0.773
## F9 0.803 0.015 0.787 0.825
## F10 0.839 0.185 0.654 0.752
## F11 0.819 0.223 0.596 0.696
## F12 0.633 0.129 0.504 0.611
include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.
Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (201 0)
This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.
## Warning in polychoric(ddNum13, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1005 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.
The chi-squared for the Bartlett test is 3.6452156^{4} with 1128 DF, p = 0e+00.
From EFAtools::KMO documentation:
The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis
The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.
## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.
[1] 0.8506322
## Warning in polychoric(imputedNumericDF13, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1005 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.
The chi-squared for the Bartlett test is 3.505972^{4} with 1128 DF, p = 0e+00.
From EFAtools::KMO documentation:
The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis
The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.
## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.
[1] 0.8506322
For factor analysis, it is recommended that some of the item
correlationsshould be between 0.3 and 0.9. Polychoric correlations were
computed using the polychoric function in the
psych package in R with options smooth = TRUE
to adjust for non-positive-definite matrices and
correct = 0.01 to avoid computation problems with
covariance of zero.
The minimum correlation in this data set is -0.477. The maximum correlation in this data set is 0.856.
#### Post-Imputation
The post imputation polyserial correlation was also computed using
the polychoric function, with no setting
smooth = TRUE and correct = 0.01.
The minimum correlation was -0.467. The maximum correlation was 0.851.
From the EFAtools documentation:
Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.
Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not
PCA) - fm = “wls” (weighted least squares because pa gave errors and
weighted recommended for ordinal data. - use = “all.obs” (since we have
imputed missing values, we can use all data points) - cor = “poly” (use
polychoric correlation matrix) - n.iter = 100 (run for 100
iterations)
The suggested number of factors is 11.
MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
## Warning in fa.stats(r = r, f = f, phi = phi, n.obs = n.obs, np.obs = np.obs, :
## The estimated weights for the factor scores are probably incorrect. Try a
## different factor score estimation method.
## Warning in fac(r = r, nfactors = nfactors, n.obs = n.obs, rotate = rotate, : An
## ultra-Heywood case was detected. Examine the results carefully
| Number of Factors | MAP value |
|---|---|
| 1 | 0.0326 |
| 2 | 0.0288 |
| 3 | 0.0221 |
| 4 | 0.0195 |
| 5 | 0.0179 |
| 6 | 0.0174 |
| 7 | 0.0168 |
| 8 | 0.0157 |
| 9 | 0.0144 |
| 10 | 0.0145 |
| 11 | 0.0144 |
| 12 | 0.0147 |
| 13 | 0.0154 |
| 14 | 0.0158 |
| 15 | 0.0167 |
| 16 | 0.0177 |
| 17 | 0.0191 |
| 18 | 0.0203 |
## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1005 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.
Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.7273123. Should be > 0.9; need reference)
| fanal13.communality | |
|---|---|
| TRAIN01 | 0.47 |
| TRAIN03 | 0.45 |
| TRAIN04 | 0.59 |
| TRAIN07 | 0.62 |
| AGG09 | 0.78 |
| AGG10 | 0.67 |
| AGG14 | 0.48 |
| AGG15 | 0.79 |
| AGG16 | 0.78 |
| AGG17 | 0.76 |
| AGG18 | 0.73 |
| AGG19 | 0.68 |
| AGG20 | 0.65 |
| FEAR21 | 0.83 |
| FEAR23 | 0.81 |
| FEAR24 | 0.87 |
| FEAR25 | 0.44 |
| FEAR26 | 0.44 |
| FEAR27 | 0.81 |
| FEAR28 | 0.65 |
| FEAR29 | 0.53 |
| FEAR30 | 0.67 |
| FEAR31 | 0.71 |
| SEPR32 | 0.67 |
| SEPR33 | 0.63 |
| SEPR34 | 0.70 |
| EXCITE35 | 0.47 |
| EXCITE36 | 0.59 |
| EXCITE37 | 0.63 |
| EXCITE38 | 0.65 |
| PLAY43 | 0.56 |
| PLAY44 | 0.80 |
| PLAY45 | 0.76 |
| PLAY46 | 0.71 |
| IMP47 | 0.51 |
| IMP48 | 0.43 |
| MISC52 | 0.52 |
| MISC53 | 0.50 |
| MISC54 | 0.66 |
| MISC55 | 0.69 |
| MISC56 | 0.60 |
| MISC59 | 0.52 |
| MISC61 | 0.51 |
| MISC62 | 0.44 |
| MISC64 | 0.65 |
| MISC65 | 0.65 |
| MISC66 | 0.69 |
| MISC67 | 0.60 |
There are 0 items with communality < 0.40.
| fanal13.communality | item |
|---|---|
| PA1 | PA12 | PA11 | PA2 | PA7 | PA8 | PA9 | PA5 | PA4 | PA3 | PA10 | PA6 | PA13 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| TRAIN01 | -0.14 | 0.05 | 0.12 | -0.08 | -0.08 | -0.04 | 0.01 | 0.02 | -0.05 | 0.60 | 0.07 | 0.03 | 0.09 |
| TRAIN03 | -0.07 | 0.03 | -0.07 | -0.09 | 0.06 | 0.08 | 0.08 | -0.05 | -0.04 | 0.62 | 0.11 | -0.03 | -0.11 |
| TRAIN04 | 0.07 | -0.06 | 0.21 | -0.04 | 0.00 | 0.01 | 0.02 | 0.01 | -0.03 | 0.65 | -0.03 | 0.01 | 0.06 |
| TRAIN07 | 0.05 | -0.10 | 0.59 | -0.10 | -0.05 | 0.00 | 0.01 | 0.02 | -0.01 | 0.29 | 0.03 | -0.05 | 0.02 |
| AGG09 | 0.22 | 0.79 | 0.02 | 0.05 | 0.08 | -0.04 | -0.04 | -0.02 | -0.05 | 0.08 | 0.04 | -0.06 | -0.04 |
| AGG10 | -0.04 | 0.78 | -0.02 | 0.06 | -0.03 | -0.01 | 0.11 | 0.03 | 0.03 | -0.06 | 0.01 | 0.05 | 0.12 |
| AGG14 | 0.04 | 0.59 | 0.09 | -0.01 | -0.01 | 0.03 | 0.11 | 0.03 | 0.07 | -0.09 | -0.09 | 0.16 | 0.15 |
| AGG15 | 0.26 | 0.75 | 0.00 | -0.05 | 0.01 | 0.00 | -0.04 | -0.11 | 0.07 | 0.00 | 0.09 | 0.04 | 0.04 |
| AGG16 | -0.15 | 0.40 | 0.03 | -0.06 | 0.08 | 0.01 | -0.05 | 0.37 | 0.38 | 0.08 | -0.04 | -0.20 | -0.14 |
| AGG17 | 0.06 | 0.28 | 0.09 | 0.12 | 0.06 | 0.10 | 0.13 | 0.01 | 0.13 | 0.01 | 0.11 | -0.15 | 0.61 |
| AGG18 | -0.17 | 0.38 | 0.02 | 0.03 | -0.01 | -0.04 | 0.00 | 0.34 | 0.43 | 0.07 | -0.02 | -0.13 | -0.09 |
| AGG19 | -0.03 | 0.11 | 0.02 | 0.02 | 0.00 | 0.11 | 0.01 | 0.04 | 0.69 | -0.02 | 0.09 | -0.16 | -0.04 |
| AGG20 | 0.06 | -0.12 | -0.01 | -0.05 | 0.01 | -0.03 | 0.01 | -0.06 | 0.84 | -0.03 | 0.05 | 0.13 | 0.09 |
| FEAR21 | 0.80 | 0.11 | 0.00 | -0.02 | 0.02 | 0.01 | 0.00 | 0.08 | 0.02 | 0.00 | 0.09 | -0.03 | 0.04 |
| FEAR23 | 0.76 | 0.16 | 0.00 | -0.03 | 0.06 | -0.01 | 0.07 | 0.15 | -0.01 | -0.01 | -0.04 | -0.05 | 0.00 |
| FEAR24 | 0.80 | 0.14 | 0.01 | -0.11 | -0.02 | 0.05 | -0.02 | 0.15 | -0.01 | -0.04 | 0.04 | -0.02 | -0.01 |
| FEAR25 | 0.33 | -0.12 | 0.17 | 0.02 | 0.30 | 0.02 | 0.04 | 0.10 | 0.10 | 0.11 | -0.03 | 0.04 | 0.10 |
| FEAR26 | 0.36 | 0.01 | 0.00 | 0.05 | -0.03 | -0.02 | 0.04 | 0.07 | 0.09 | 0.00 | 0.42 | 0.04 | 0.01 |
| FEAR27 | 0.18 | -0.04 | 0.01 | 0.02 | 0.02 | 0.00 | 0.02 | 0.83 | 0.04 | -0.02 | 0.01 | 0.04 | 0.02 |
| FEAR28 | 0.47 | -0.12 | 0.10 | 0.04 | 0.37 | 0.05 | 0.03 | 0.06 | 0.02 | 0.03 | 0.15 | -0.10 | 0.06 |
| FEAR29 | -0.05 | 0.04 | -0.01 | 0.00 | -0.05 | 0.01 | 0.01 | 0.04 | -0.03 | 0.04 | 0.73 | 0.02 | 0.05 |
| FEAR30 | -0.03 | -0.02 | 0.01 | 0.02 | 0.08 | -0.02 | 0.05 | 0.00 | 0.06 | -0.01 | 0.77 | 0.03 | -0.02 |
| FEAR31 | 0.11 | -0.11 | 0.02 | 0.02 | 0.05 | 0.00 | 0.03 | 0.79 | -0.07 | 0.01 | 0.10 | 0.06 | 0.01 |
| SEPR32 | 0.09 | -0.01 | 0.00 | -0.06 | -0.04 | 0.07 | 0.79 | 0.00 | 0.05 | -0.06 | 0.04 | -0.08 | -0.01 |
| SEPR33 | -0.07 | -0.02 | 0.01 | -0.03 | 0.03 | -0.01 | 0.78 | 0.04 | -0.04 | 0.01 | 0.06 | -0.01 | -0.06 |
| SEPR34 | -0.07 | 0.02 | 0.00 | -0.01 | 0.05 | -0.04 | 0.82 | 0.03 | -0.04 | 0.07 | -0.02 | 0.04 | 0.13 |
| EXCITE35 | 0.10 | 0.02 | 0.05 | -0.10 | -0.09 | 0.64 | 0.15 | 0.00 | -0.03 | -0.02 | -0.01 | -0.01 | -0.12 |
| EXCITE36 | 0.01 | 0.00 | 0.04 | 0.18 | 0.01 | 0.70 | -0.05 | -0.09 | -0.03 | -0.03 | 0.06 | -0.04 | -0.01 |
| EXCITE37 | -0.02 | 0.01 | 0.00 | -0.08 | -0.01 | 0.82 | 0.01 | 0.02 | 0.00 | 0.01 | -0.03 | 0.02 | 0.02 |
| EXCITE38 | -0.02 | -0.07 | -0.11 | 0.04 | 0.07 | 0.77 | -0.04 | 0.03 | 0.04 | 0.05 | -0.02 | 0.06 | 0.09 |
| PLAY43 | -0.28 | -0.24 | 0.00 | 0.52 | 0.02 | 0.08 | -0.05 | 0.07 | -0.08 | -0.08 | 0.00 | 0.03 | -0.11 |
| PLAY44 | -0.02 | -0.03 | -0.02 | 0.85 | -0.03 | 0.05 | -0.04 | 0.00 | 0.07 | 0.00 | 0.04 | -0.10 | 0.00 |
| PLAY45 | -0.02 | 0.06 | -0.01 | 0.85 | -0.05 | 0.01 | -0.05 | 0.06 | -0.09 | -0.11 | -0.01 | 0.01 | 0.00 |
| PLAY46 | -0.04 | 0.09 | -0.16 | 0.75 | 0.01 | 0.02 | 0.03 | -0.05 | -0.02 | 0.05 | -0.05 | -0.03 | 0.12 |
| IMP47 | 0.12 | 0.00 | -0.03 | 0.35 | 0.01 | 0.09 | 0.06 | 0.03 | 0.14 | 0.38 | -0.05 | 0.34 | -0.05 |
| IMP48 | 0.08 | 0.01 | 0.04 | 0.25 | 0.05 | 0.10 | 0.11 | 0.02 | 0.16 | 0.25 | -0.01 | 0.33 | -0.13 |
| MISC52 | -0.11 | 0.14 | 0.08 | -0.15 | 0.03 | 0.08 | -0.05 | 0.14 | -0.03 | -0.06 | 0.09 | 0.64 | -0.01 |
| MISC53 | -0.12 | 0.06 | -0.03 | -0.13 | -0.01 | 0.03 | 0.04 | 0.02 | 0.04 | 0.10 | 0.12 | 0.60 | -0.12 |
| MISC54 | -0.02 | -0.03 | 0.14 | -0.06 | 0.70 | 0.06 | -0.04 | 0.03 | 0.00 | 0.00 | 0.07 | 0.06 | 0.09 |
| MISC55 | -0.03 | 0.01 | -0.07 | 0.00 | 0.85 | -0.01 | 0.05 | -0.01 | 0.01 | -0.03 | -0.01 | -0.06 | -0.03 |
| MISC56 | -0.05 | 0.06 | 0.01 | -0.02 | 0.78 | -0.02 | -0.01 | 0.01 | -0.02 | 0.01 | 0.00 | 0.06 | -0.02 |
| MISC59 | 0.15 | -0.05 | 0.15 | 0.30 | 0.02 | 0.02 | 0.37 | -0.13 | 0.16 | 0.11 | 0.00 | 0.19 | -0.22 |
| MISC61 | 0.05 | 0.11 | 0.08 | 0.40 | -0.07 | 0.23 | 0.22 | -0.16 | -0.02 | -0.07 | -0.06 | -0.04 | -0.31 |
| MISC62 | -0.11 | 0.13 | 0.41 | 0.02 | 0.00 | 0.08 | 0.01 | 0.30 | 0.09 | 0.06 | 0.01 | -0.02 | -0.19 |
| MISC64 | -0.11 | 0.03 | 0.82 | -0.01 | -0.02 | -0.02 | 0.03 | -0.02 | -0.01 | -0.03 | 0.00 | 0.01 | 0.11 |
| MISC65 | -0.10 | 0.03 | 0.71 | -0.03 | -0.01 | -0.01 | 0.02 | 0.06 | 0.03 | 0.10 | 0.05 | 0.04 | -0.02 |
| MISC66 | 0.23 | -0.01 | 0.58 | -0.04 | 0.21 | -0.05 | 0.03 | -0.03 | -0.05 | 0.09 | 0.06 | 0.01 | -0.08 |
| MISC67 | 0.22 | 0.00 | 0.58 | -0.08 | 0.17 | -0.03 | 0.05 | 0.00 | 0.03 | -0.05 | 0.01 | 0.03 | -0.08 |
| largest | maximum | itemNames | itemDescriptions | |
|---|---|---|---|---|
| 14 | PA1 | 0.80 | FEAR21 | When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel |
| 15 | PA1 | 0.76 | FEAR23 | When an unfamiliar person visits your home or approaches the dog when in his/her home kennel |
| 16 | PA1 | 0.80 | FEAR24 | When an unfamiliar person tries to touch or pet the dog |
| 17 | PA1 | 0.33 | FEAR25 | In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc. |
| 20 | PA1 | 0.47 | FEAR28 | When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.) |
| 18 | PA10 | 0.42 | FEAR26 | When examined/treated by a veterinarian |
| 21 | PA10 | 0.73 | FEAR29 | When having nails trimmed, or feet touched/handled |
| 22 | PA10 | 0.77 | FEAR30 | When groomed or bathed |
| 33 | PA11 | 0.41 | MISC62 | Becomes highly excited and/or distracted when encountering unfamiliar dogs |
| 34 | PA11 | 0.82 | MISC64 | When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects |
| 35 | PA11 | 0.71 | MISC65 | Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.) |
| 36 | PA11 | 0.58 | MISC66 | Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work |
| 37 | PA11 | 0.58 | MISC67 | Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work |
| 48 | PA11 | 0.59 | TRAIN07 | Unfocused; is easily distracted by interesting sights, sounds or smells |
| 1 | PA12 | 0.79 | AGG09 | Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash |
| 2 | PA12 | 0.78 | AGG10 | Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel |
| 3 | PA12 | 0.59 | AGG14 | When strangers walk past when the dog is in his/her home run or kennel |
| 4 | PA12 | 0.75 | AGG15 | When an unfamiliar person tries to touch or pet the dog |
| 5 | PA12 | 0.40 | AGG16 | When approached directly by an unfamiliar dog while being walked/exercised on a leash |
| 6 | PA13 | 0.61 | AGG17 | When stared at directly by you or another familiar person |
| 32 | PA2 | 0.40 | MISC61 | Active, energetic, always on the go |
| 38 | PA2 | 0.52 | PLAY43 | Eagerly engages in play with new/unfamiliar people |
| 39 | PA2 | 0.85 | PLAY44 | Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person |
| 40 | PA2 | 0.85 | PLAY45 | Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown |
| 41 | PA2 | 0.75 | PLAY46 | Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task |
| 24 | PA3 | 0.38 | IMP47 | Impulsive; doesn’t seem to think before s/he acts |
| 45 | PA3 | 0.60 | TRAIN01 | Is hard to recall when off the leash |
| 46 | PA3 | 0.62 | TRAIN03 | Is slow to obey a ‘stay’ command |
| 47 | PA3 | 0.65 | TRAIN04 | Has difficulty attending/listening to things you say or do |
| 7 | PA4 | 0.43 | AGG18 | When barked, growled, or lunged at by another dog |
| 8 | PA4 | 0.69 | AGG19 | Towards other familiar dogs |
| 9 | PA4 | 0.84 | AGG20 | When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog |
| 19 | PA5 | 0.83 | FEAR27 | When approached directly by an unfamiliar dog |
| 23 | PA5 | 0.79 | FEAR31 | When barked, growled, or lunged at by an unfamiliar dog |
| 25 | PA6 | 0.33 | IMP48 | Becomes frustrated/impatient in a wide range of situations |
| 26 | PA6 | 0.64 | MISC52 | Begs persistently for food when people are eating |
| 27 | PA6 | 0.60 | MISC53 | Steals food |
| 28 | PA7 | 0.70 | MISC54 | Reluctant to/nervous about crossing grates or other unfamiliar surfaces |
| 29 | PA7 | 0.85 | MISC55 | Reluctant to/nervous about crossing shiny or slippery floors |
| 30 | PA7 | 0.78 | MISC56 | Nervous or frightened when ascending or descending some types of stairs |
| 10 | PA8 | 0.64 | EXCITE35 | Excitable when you first arrive home, or at the dog’s kennel, after a brief absence |
| 11 | PA8 | 0.70 | EXCITE36 | Excitable when playing with you or other familiar persons |
| 12 | PA8 | 0.82 | EXCITE37 | Excitable just before being taken out for a walk |
| 13 | PA8 | 0.77 | EXCITE38 | Excitable just before being taken out for work or training |
| 31 | PA9 | 0.37 | MISC59 | Hyperactive, restless, has trouble settling down |
| 42 | PA9 | 0.79 | SEPR32 | Restlessness/agitation/pacing when left alone |
| 43 | PA9 | 0.78 | SEPR33 | Barking or whining when left alone |
| 44 | PA9 | 0.82 | SEPR34 | Chewing/scratching at doors, floor, fencing, etc., when left alone |
| PA1 | PA12 | PA11 | PA2 | PA7 | PA8 | PA9 | PA5 | PA4 | PA3 | PA10 | PA6 | PA13 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| alpha | 0.817 | 0.751 | 0.787 | 0.8 | 0.718 | 0.787 | 0.718 | 0.804 | 0.626 | 0.618 | 0.616 | 0.54 | 1 |
omega is thought to be better measure of reliability than alpha, because it looks at the relationships between all the items rather than just the ones within each factor. It’s different than alpha because it assumes that there is a genral factor, g, that all items have in common. This is listed as the first row of the table below.
There are three omegas for each factor:
From EFAtools::OMEGA documentation:
Omegas refer to the correlation between a factor and a unit-weighted composite score and thus the true score variance in a unit-weighted composite based on the respective indicators. Omega total is the total true score variance in a composite. Omega hierarchical is the true score variance in a composite that is attributable to the general factor, and omega subscale is the true score variance in a composite attributable to all subscales / group factors (for the whole scale) or to the specific subscale / group factor (for subscale composites).
Interpretation of omega_subscale
no universal guideline
0.50 is minimum, 0.75 preferable (watkins books,rodrigues16, zimbarg2005
## Omega total, omega hierarchical, omega subscale, H index, explained common variance (ECV), and percent of uncontaminated correlations (PUC) for the general factor (top row) and omegas and H index for the group factors:
##
## tot hier sub H ECV PUC
## g 0.947 0.565 0.203 0.883 0.249 0.933
## F1 0.820 0.344 0.476 0.773
## F2 0.739 0.303 0.436 0.586
## F3 0.816 0.350 0.466 0.724
## F4 0.798 0.189 0.609 0.802
## F5 0.519 0.151 0.368 0.368
## F6 0.772 0.055 0.717 0.868
## F7 0.665 0.141 0.525 0.624
## F8 0.701 0.178 0.523 0.705
## F9 0.827 0.237 0.590 0.692
## F10 0.577 0.089 0.488 0.573
## F11 0.830 0.216 0.614 0.731
## F12 0.822 0.014 0.809 0.831
## F13 0.798 0.155 0.643 0.791
include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.
Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (201 0)
This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.
## Warning in polychoric(ddNum14, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 991 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.
The chi-squared for the Bartlett test is 3.5499905^{4} with 1128 DF, p = 0e+00.
From EFAtools::KMO documentation:
The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis
The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.
## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.
[1] 0.8491539
## Warning in polychoric(imputedNumericDF14, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 991 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.
The chi-squared for the Bartlett test is 3.4280193^{4} with 1128 DF, p = 0e+00.
From EFAtools::KMO documentation:
The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis
The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.
## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.
[1] 0.8491539
For factor analysis, it is recommended that some of the item
correlationsshould be between 0.3 and 0.9. Polychoric correlations were
computed using the polychoric function in the
psych package in R with options smooth = TRUE
to adjust for non-positive-definite matrices and
correct = 0.01 to avoid computation problems with
covariance of zero.
The minimum correlation in this data set is -0.477. The maximum correlation in this data set is 0.856.
#### Post-Imputation
The post imputation polyserial correlation was also computed using
the polychoric function, with no setting
smooth = TRUE and correct = 0.01.
The minimum correlation was -0.466. The maximum correlation was 0.851.
From the EFAtools documentation:
Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.
Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not
PCA) - fm = “wls” (weighted least squares because pa gave errors and
weighted recommended for ordinal data. - use = “all.obs” (since we have
imputed missing values, we can use all data points) - cor = “poly” (use
polychoric correlation matrix) - n.iter = 100 (run for 100
iterations)
The suggested number of factors is 11.
MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.
| Number of Factors | MAP value |
|---|---|
| 1 | 0.0327 |
| 2 | 0.0280 |
| 3 | 0.0219 |
| 4 | 0.0192 |
| 5 | 0.0174 |
| 6 | 0.0168 |
| 7 | 0.0164 |
| 8 | 0.0155 |
| 9 | 0.0143 |
| 10 | 0.0145 |
| 11 | 0.0145 |
| 12 | 0.0145 |
| 13 | 0.0148 |
| 14 | 0.0152 |
| 15 | 0.0163 |
| 16 | 0.0173 |
| 17 | 0.0184 |
| 18 | 0.0197 |
## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 991 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.
Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.7598549. Should be > 0.9; need reference)
| fanal14.communality | |
|---|---|
| TRAIN01 | 0.50 |
| TRAIN03 | 0.45 |
| TRAIN04 | 0.59 |
| TRAIN07 | 0.62 |
| AGG09 | 0.78 |
| AGG10 | 0.70 |
| AGG14 | 0.51 |
| AGG15 | 0.77 |
| AGG16 | 0.76 |
| AGG18 | 0.72 |
| AGG19 | 0.76 |
| AGG20 | 0.56 |
| FEAR21 | 0.83 |
| FEAR23 | 0.82 |
| FEAR24 | 0.88 |
| FEAR25 | 0.44 |
| FEAR26 | 0.44 |
| FEAR27 | 0.80 |
| FEAR28 | 0.65 |
| FEAR29 | 0.61 |
| FEAR30 | 0.62 |
| FEAR31 | 0.72 |
| SEPR32 | 0.68 |
| SEPR33 | 0.66 |
| SEPR34 | 0.65 |
| EXCITE35 | 0.46 |
| EXCITE36 | 0.58 |
| EXCITE37 | 0.64 |
| EXCITE38 | 0.65 |
| PLAY43 | 0.55 |
| PLAY44 | 0.83 |
| PLAY45 | 0.76 |
| PLAY46 | 0.74 |
| IMP47 | 0.59 |
| IMP48 | 0.60 |
| MISC52 | 0.62 |
| MISC53 | 0.55 |
| MISC54 | 0.65 |
| MISC55 | 0.71 |
| MISC56 | 0.62 |
| MISC59 | 0.57 |
| MISC60 | 0.58 |
| MISC61 | 0.71 |
| MISC62 | 0.45 |
| MISC64 | 0.60 |
| MISC65 | 0.65 |
| MISC66 | 0.69 |
| MISC67 | 0.60 |
There are 0 items with communality < 0.40.
| fanal14.communality | item |
|---|---|
| PA1 | PA3 | PA13 | PA2 | PA5 | PA8 | PA7 | PA4 | PA9 | PA10 | PA11 | PA14 | PA12 | PA6 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| TRAIN01 | -0.06 | 0.10 | 0.00 | -0.02 | -0.05 | -0.06 | 0.02 | 0.00 | -0.01 | 0.06 | 0.61 | 0.00 | 0.01 | 0.11 |
| TRAIN03 | -0.01 | -0.05 | -0.04 | -0.04 | 0.07 | 0.07 | 0.10 | 0.02 | -0.05 | 0.06 | 0.60 | 0.05 | 0.03 | 0.04 |
| TRAIN04 | 0.06 | 0.24 | -0.04 | -0.03 | -0.01 | 0.03 | 0.03 | -0.06 | 0.00 | -0.02 | 0.56 | 0.18 | -0.08 | -0.03 |
| TRAIN07 | 0.06 | 0.62 | -0.09 | -0.05 | -0.06 | 0.01 | 0.03 | 0.00 | 0.00 | 0.01 | 0.27 | 0.01 | -0.05 | -0.01 |
| AGG09 | 0.21 | 0.02 | 0.76 | 0.01 | 0.07 | -0.04 | -0.06 | -0.02 | -0.01 | 0.04 | 0.08 | 0.05 | 0.07 | -0.08 |
| AGG10 | -0.07 | -0.01 | 0.83 | 0.06 | -0.03 | 0.02 | 0.11 | 0.01 | 0.02 | 0.05 | -0.06 | 0.03 | -0.06 | -0.01 |
| AGG14 | 0.04 | 0.12 | 0.65 | 0.07 | -0.02 | 0.07 | 0.13 | 0.03 | 0.00 | -0.06 | -0.08 | 0.00 | -0.13 | 0.12 |
| AGG15 | 0.29 | -0.02 | 0.69 | -0.06 | 0.03 | -0.02 | -0.06 | 0.11 | -0.13 | 0.07 | 0.02 | -0.01 | 0.07 | 0.05 |
| AGG16 | -0.10 | 0.04 | 0.31 | -0.05 | 0.07 | 0.00 | -0.04 | 0.49 | 0.37 | -0.07 | 0.10 | -0.04 | 0.02 | -0.10 |
| AGG18 | -0.13 | -0.01 | 0.30 | -0.03 | 0.00 | -0.07 | -0.03 | 0.51 | 0.34 | -0.04 | 0.07 | 0.04 | 0.10 | -0.06 |
| AGG19 | 0.06 | 0.02 | 0.00 | 0.07 | 0.02 | 0.07 | 0.02 | 0.84 | -0.01 | 0.05 | 0.03 | -0.07 | 0.03 | -0.02 |
| AGG20 | 0.03 | -0.01 | -0.08 | -0.04 | 0.01 | -0.01 | 0.02 | 0.72 | -0.09 | 0.07 | -0.08 | 0.18 | -0.14 | 0.09 |
| FEAR21 | 0.84 | 0.00 | 0.08 | -0.01 | 0.02 | 0.00 | -0.01 | 0.01 | 0.05 | 0.07 | 0.00 | 0.02 | 0.02 | -0.02 |
| FEAR23 | 0.80 | 0.00 | 0.12 | -0.01 | 0.05 | -0.02 | 0.07 | 0.00 | 0.12 | -0.06 | 0.00 | 0.00 | 0.01 | -0.04 |
| FEAR24 | 0.87 | 0.01 | 0.08 | -0.07 | -0.03 | 0.04 | -0.02 | 0.01 | 0.11 | 0.01 | -0.02 | -0.04 | 0.01 | 0.02 |
| FEAR25 | 0.36 | 0.20 | -0.11 | 0.08 | 0.29 | 0.03 | 0.06 | 0.08 | 0.05 | -0.03 | 0.08 | 0.04 | -0.10 | 0.05 |
| FEAR26 | 0.40 | 0.00 | -0.01 | 0.07 | -0.02 | -0.03 | 0.04 | 0.11 | 0.05 | 0.39 | 0.01 | 0.00 | 0.01 | 0.06 |
| FEAR27 | 0.20 | 0.00 | -0.04 | 0.01 | 0.02 | -0.01 | 0.02 | 0.06 | 0.79 | 0.02 | -0.02 | 0.01 | -0.03 | 0.05 |
| FEAR28 | 0.48 | 0.13 | -0.10 | 0.06 | 0.36 | 0.05 | 0.04 | 0.01 | 0.04 | 0.14 | 0.01 | 0.04 | -0.08 | -0.10 |
| FEAR29 | -0.07 | -0.02 | 0.08 | -0.04 | -0.04 | 0.02 | 0.00 | -0.04 | 0.05 | 0.80 | 0.04 | -0.02 | 0.03 | 0.00 |
| FEAR30 | -0.01 | 0.04 | -0.02 | 0.01 | 0.08 | -0.01 | 0.07 | 0.10 | 0.02 | 0.70 | -0.02 | 0.03 | -0.04 | 0.04 |
| FEAR31 | 0.09 | 0.01 | -0.07 | -0.02 | 0.05 | 0.02 | 0.03 | -0.07 | 0.78 | 0.12 | -0.01 | 0.06 | -0.06 | 0.03 |
| SEPR32 | 0.08 | 0.01 | 0.02 | -0.06 | -0.05 | 0.08 | 0.78 | 0.05 | 0.00 | 0.04 | -0.07 | 0.03 | 0.01 | -0.08 |
| SEPR33 | -0.06 | 0.03 | 0.00 | 0.02 | 0.02 | 0.00 | 0.80 | -0.03 | 0.04 | 0.03 | 0.03 | -0.01 | 0.01 | 0.01 |
| SEPR34 | -0.03 | -0.01 | 0.05 | 0.01 | 0.06 | -0.04 | 0.78 | -0.03 | 0.00 | -0.01 | 0.08 | 0.00 | 0.04 | 0.06 |
| EXCITE35 | 0.13 | 0.04 | -0.03 | -0.09 | -0.09 | 0.59 | 0.14 | 0.03 | 0.00 | -0.04 | 0.01 | -0.05 | 0.14 | 0.05 |
| EXCITE36 | 0.01 | 0.03 | 0.01 | 0.13 | 0.02 | 0.65 | -0.06 | -0.01 | -0.07 | 0.06 | -0.03 | 0.03 | 0.13 | -0.04 |
| EXCITE37 | -0.03 | 0.01 | 0.04 | -0.06 | -0.02 | 0.81 | 0.02 | 0.01 | 0.02 | -0.01 | 0.01 | 0.01 | 0.00 | 0.01 |
| EXCITE38 | -0.03 | -0.09 | -0.01 | 0.05 | 0.06 | 0.77 | -0.02 | 0.02 | 0.02 | 0.00 | 0.02 | 0.07 | -0.05 | 0.01 |
| PLAY43 | -0.28 | 0.02 | -0.24 | 0.50 | 0.01 | 0.07 | -0.04 | -0.07 | 0.09 | -0.01 | -0.08 | 0.02 | 0.07 | 0.03 |
| PLAY44 | 0.00 | 0.03 | -0.03 | 0.85 | -0.03 | 0.04 | -0.02 | 0.09 | 0.00 | 0.04 | 0.00 | 0.06 | 0.03 | -0.10 |
| PLAY45 | 0.02 | 0.01 | 0.04 | 0.82 | -0.04 | -0.02 | -0.05 | -0.06 | 0.06 | -0.02 | -0.09 | 0.01 | 0.09 | 0.02 |
| PLAY46 | 0.01 | -0.13 | 0.10 | 0.82 | 0.02 | 0.01 | 0.06 | 0.00 | -0.09 | -0.05 | 0.07 | -0.01 | -0.02 | 0.01 |
| IMP47 | 0.01 | -0.07 | 0.04 | 0.11 | -0.02 | 0.07 | -0.02 | 0.00 | 0.05 | -0.01 | 0.16 | 0.64 | 0.06 | 0.07 |
| IMP48 | -0.09 | 0.03 | 0.08 | 0.00 | -0.01 | 0.09 | 0.03 | 0.00 | 0.06 | 0.02 | 0.00 | 0.71 | 0.00 | 0.03 |
| MISC52 | 0.00 | 0.06 | 0.07 | -0.02 | 0.04 | 0.04 | -0.04 | -0.03 | 0.08 | 0.01 | -0.04 | -0.02 | 0.00 | 0.76 |
| MISC53 | -0.01 | -0.06 | -0.06 | -0.03 | -0.01 | -0.02 | 0.04 | 0.07 | -0.03 | 0.02 | 0.11 | 0.08 | 0.02 | 0.68 |
| MISC54 | 0.00 | 0.16 | 0.00 | -0.03 | 0.69 | 0.07 | -0.02 | -0.01 | 0.01 | 0.08 | -0.01 | 0.00 | -0.09 | 0.06 |
| MISC55 | 0.00 | -0.06 | 0.00 | 0.03 | 0.86 | 0.00 | 0.06 | 0.04 | 0.00 | -0.01 | 0.01 | -0.07 | 0.01 | -0.02 |
| MISC56 | -0.06 | -0.01 | 0.04 | -0.09 | 0.78 | -0.04 | -0.04 | -0.03 | 0.02 | 0.01 | -0.01 | 0.08 | 0.08 | 0.03 |
| MISC59 | 0.07 | 0.09 | -0.09 | 0.03 | 0.00 | -0.06 | 0.26 | 0.10 | -0.09 | 0.01 | -0.02 | 0.41 | 0.34 | 0.04 |
| MISC60 | -0.02 | 0.01 | -0.06 | 0.04 | 0.06 | 0.08 | 0.00 | -0.12 | 0.02 | 0.04 | 0.03 | 0.05 | 0.70 | 0.03 |
| MISC61 | 0.05 | 0.00 | 0.00 | 0.15 | -0.04 | 0.10 | 0.11 | 0.04 | -0.10 | -0.05 | -0.05 | 0.03 | 0.69 | -0.03 |
| MISC62 | -0.09 | 0.38 | 0.05 | -0.06 | 0.00 | 0.03 | -0.02 | 0.16 | 0.32 | -0.01 | 0.06 | 0.01 | 0.22 | 0.04 |
| MISC64 | -0.10 | 0.78 | 0.06 | 0.00 | 0.00 | -0.03 | 0.03 | 0.00 | -0.03 | 0.02 | 0.01 | -0.07 | 0.02 | 0.04 |
| MISC65 | -0.09 | 0.71 | 0.03 | -0.02 | -0.02 | -0.01 | 0.02 | 0.06 | 0.05 | 0.03 | 0.10 | 0.01 | 0.02 | 0.07 |
| MISC66 | 0.19 | 0.62 | 0.00 | -0.05 | 0.17 | -0.04 | 0.03 | -0.07 | -0.02 | 0.04 | 0.03 | 0.11 | -0.04 | -0.03 |
| MISC67 | 0.16 | 0.60 | 0.02 | -0.13 | 0.14 | -0.02 | 0.04 | -0.01 | 0.02 | 0.02 | -0.10 | 0.10 | 0.01 | -0.02 |
| largest | maximum | itemNames | itemDescriptions | |
|---|---|---|---|---|
| 13 | PA1 | 0.84 | FEAR21 | When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel |
| 14 | PA1 | 0.80 | FEAR23 | When an unfamiliar person visits your home or approaches the dog when in his/her home kennel |
| 15 | PA1 | 0.87 | FEAR24 | When an unfamiliar person tries to touch or pet the dog |
| 16 | PA1 | 0.36 | FEAR25 | In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc. |
| 17 | PA1 | 0.40 | FEAR26 | When examined/treated by a veterinarian |
| 19 | PA1 | 0.48 | FEAR28 | When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.) |
| 20 | PA10 | 0.80 | FEAR29 | When having nails trimmed, or feet touched/handled |
| 21 | PA10 | 0.70 | FEAR30 | When groomed or bathed |
| 45 | PA11 | 0.61 | TRAIN01 | Is hard to recall when off the leash |
| 46 | PA11 | 0.60 | TRAIN03 | Is slow to obey a ‘stay’ command |
| 47 | PA11 | 0.56 | TRAIN04 | Has difficulty attending/listening to things you say or do |
| 31 | PA12 | 0.70 | MISC60 | Playful, puppyish, boisterous |
| 32 | PA12 | 0.69 | MISC61 | Active, energetic, always on the go |
| 1 | PA13 | 0.76 | AGG09 | Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash |
| 2 | PA13 | 0.83 | AGG10 | Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel |
| 3 | PA13 | 0.65 | AGG14 | When strangers walk past when the dog is in his/her home run or kennel |
| 4 | PA13 | 0.69 | AGG15 | When an unfamiliar person tries to touch or pet the dog |
| 23 | PA14 | 0.64 | IMP47 | Impulsive; doesn’t seem to think before s/he acts |
| 24 | PA14 | 0.71 | IMP48 | Becomes frustrated/impatient in a wide range of situations |
| 30 | PA14 | 0.41 | MISC59 | Hyperactive, restless, has trouble settling down |
| 38 | PA2 | 0.50 | PLAY43 | Eagerly engages in play with new/unfamiliar people |
| 39 | PA2 | 0.85 | PLAY44 | Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person |
| 40 | PA2 | 0.82 | PLAY45 | Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown |
| 41 | PA2 | 0.82 | PLAY46 | Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task |
| 33 | PA3 | 0.38 | MISC62 | Becomes highly excited and/or distracted when encountering unfamiliar dogs |
| 34 | PA3 | 0.78 | MISC64 | When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects |
| 35 | PA3 | 0.71 | MISC65 | Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.) |
| 36 | PA3 | 0.62 | MISC66 | Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work |
| 37 | PA3 | 0.60 | MISC67 | Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work |
| 48 | PA3 | 0.62 | TRAIN07 | Unfocused; is easily distracted by interesting sights, sounds or smells |
| 5 | PA4 | 0.49 | AGG16 | When approached directly by an unfamiliar dog while being walked/exercised on a leash |
| 6 | PA4 | 0.51 | AGG18 | When barked, growled, or lunged at by another dog |
| 7 | PA4 | 0.84 | AGG19 | Towards other familiar dogs |
| 8 | PA4 | 0.72 | AGG20 | When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog |
| 27 | PA5 | 0.69 | MISC54 | Reluctant to/nervous about crossing grates or other unfamiliar surfaces |
| 28 | PA5 | 0.86 | MISC55 | Reluctant to/nervous about crossing shiny or slippery floors |
| 29 | PA5 | 0.78 | MISC56 | Nervous or frightened when ascending or descending some types of stairs |
| 25 | PA6 | 0.76 | MISC52 | Begs persistently for food when people are eating |
| 26 | PA6 | 0.68 | MISC53 | Steals food |
| 42 | PA7 | 0.78 | SEPR32 | Restlessness/agitation/pacing when left alone |
| 43 | PA7 | 0.80 | SEPR33 | Barking or whining when left alone |
| 44 | PA7 | 0.78 | SEPR34 | Chewing/scratching at doors, floor, fencing, etc., when left alone |
| 9 | PA8 | 0.59 | EXCITE35 | Excitable when you first arrive home, or at the dog’s kennel, after a brief absence |
| 10 | PA8 | 0.65 | EXCITE36 | Excitable when playing with you or other familiar persons |
| 11 | PA8 | 0.81 | EXCITE37 | Excitable just before being taken out for a walk |
| 12 | PA8 | 0.77 | EXCITE38 | Excitable just before being taken out for work or training |
| 18 | PA9 | 0.79 | FEAR27 | When approached directly by an unfamiliar dog |
| 22 | PA9 | 0.78 | FEAR31 | When barked, growled, or lunged at by an unfamiliar dog |
| PA1 | PA3 | PA13 | PA2 | PA5 | PA8 | PA7 | PA4 | PA9 | PA10 | PA11 | PA14 | PA12 | PA6 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| alpha | 0.797 | 0.787 | 0.76 | 0.812 | 0.718 | 0.787 | 0.735 | 0.753 | 0.802 | 0.616 | 0.652 | 0.682 | 0.71 | 0.623 |
omega is thought to be better measure of reliability than alpha, because it looks at the relationships between all the items rather than just the ones within each factor. It’s different than alpha because it assumes that there is a genral factor, g, that all items have in common. This is listed as the first row of the table below.
There are three omegas for each factor:
From EFAtools::OMEGA documentation:
Omegas refer to the correlation between a factor and a unit-weighted composite score and thus the true score variance in a unit-weighted composite based on the respective indicators. Omega total is the total true score variance in a composite. Omega hierarchical is the true score variance in a composite that is attributable to the general factor, and omega subscale is the true score variance in a composite attributable to all subscales / group factors (for the whole scale) or to the specific subscale / group factor (for subscale composites).
Interpretation of omega_subscale
no universal guideline
0.50 is minimum, 0.75 preferable (watkins books,rodrigues16, zimbarg2005
## Omega total, omega hierarchical, omega subscale, H index, explained common variance (ECV), and percent of uncontaminated correlations (PUC) for the general factor (top row) and omegas and H index for the group factors:
##
## tot hier sub H ECV PUC
## g 0.946 0.566 0.208 0.879 0.229 0.938
## F1 0.834 0.326 0.508 0.818
## F2 0.752 0.230 0.522 0.596
## F3 0.641 0.164 0.477 0.573
## F4 0.596 0.001 0.595 0.649
## F5 0.814 0.120 0.694 0.816
## F6 0.597 0.159 0.438 0.588
## F7 0.809 0.065 0.744 0.858
## F8 0.829 0.387 0.442 0.702
## F9 0.703 0.157 0.546 0.759
## F10 0.835 0.199 0.637 0.749
## F11 0.709 0.078 0.630 0.662
## F12 0.843 0.162 0.681 0.764
## F13 0.774 0.021 0.754 0.818
## F14 0.802 0.214 0.588 0.688
include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.
Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (201 0)
This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.
## Warning in polychoric(ddNum15, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1102 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.
The chi-squared for the Bartlett test is 3.6576356^{4} with 1275 DF, p = 0e+00.
From EFAtools::KMO documentation:
The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis
The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.
## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.
[1] 0.8460796
## Warning in polychoric(imputedNumericDF15, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1102 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.
The chi-squared for the Bartlett test is 3.5265375^{4} with 1275 DF, p = 0e+00.
From EFAtools::KMO documentation:
The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis
The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.
## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.
[1] 0.8460796
For factor analysis, it is recommended that some of the item
correlationsshould be between 0.3 and 0.9. Polychoric correlations were
computed using the polychoric function in the
psych package in R with options smooth = TRUE
to adjust for non-positive-definite matrices and
correct = 0.01 to avoid computation problems with
covariance of zero.
The minimum correlation in this data set is -0.477. The maximum correlation in this data set is 0.856.
#### Post-Imputation
The post imputation polyserial correlation was also computed using
the polychoric function, with no setting
smooth = TRUE and correct = 0.01.
The minimum correlation was -0.466. The maximum correlation was 0.851.
From the EFAtools documentation:
Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.
Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not
PCA) - fm = “wls” (weighted least squares because pa gave errors and
weighted recommended for ordinal data. - use = “all.obs” (since we have
imputed missing values, we can use all data points) - cor = “poly” (use
polychoric correlation matrix) - n.iter = 100 (run for 100
iterations)
The suggested number of factors is 12.
MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.
| Number of Factors | MAP value |
|---|---|
| 1 | 0.0302 |
| 2 | 0.0256 |
| 3 | 0.0198 |
| 4 | 0.0176 |
| 5 | 0.0163 |
| 6 | 0.0158 |
| 7 | 0.0157 |
| 8 | 0.0147 |
| 9 | 0.0142 |
| 10 | 0.0137 |
| 11 | 0.0134 |
| 12 | 0.0137 |
| 13 | 0.0138 |
| 14 | 0.0141 |
| 15 | 0.0150 |
| 16 | 0.0154 |
| 17 | 0.0163 |
| 18 | 0.0176 |
## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1102 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.
Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.747881. Should be > 0.9; need reference)
| fanal15.communality | |
|---|---|
| TRAIN01 | 0.44 |
| TRAIN02 | 0.41 |
| TRAIN03 | 0.60 |
| TRAIN04 | 0.61 |
| TRAIN07 | 0.62 |
| AGG09 | 0.76 |
| AGG10 | 0.70 |
| AGG14 | 0.51 |
| AGG15 | 0.80 |
| AGG16 | 0.76 |
| AGG18 | 0.74 |
| AGG19 | 0.77 |
| AGG20 | 0.52 |
| FEAR21 | 0.84 |
| FEAR23 | 0.81 |
| FEAR24 | 0.89 |
| FEAR26 | 0.46 |
| FEAR27 | 0.85 |
| FEAR28 | 0.63 |
| FEAR29 | 0.53 |
| FEAR30 | 0.62 |
| FEAR31 | 0.71 |
| SEPR32 | 0.68 |
| SEPR33 | 0.65 |
| SEPR34 | 0.67 |
| EXCITE35 | 0.48 |
| EXCITE36 | 0.58 |
| EXCITE37 | 0.65 |
| EXCITE38 | 0.66 |
| ATT39 | 0.52 |
| ATT41 | 0.33 |
| PLAY43 | 0.55 |
| PLAY44 | 0.84 |
| PLAY45 | 0.76 |
| PLAY46 | 0.72 |
| IMP47 | 0.57 |
| IMP48 | 0.62 |
| MISC52 | 0.52 |
| MISC53 | 0.61 |
| MISC54 | 0.64 |
| MISC55 | 0.79 |
| MISC56 | 0.60 |
| MISC59 | 0.59 |
| MISC60 | 0.61 |
| MISC61 | 0.70 |
| MISC62 | 0.45 |
| MISC64 | 0.61 |
| MISC65 | 0.65 |
| MISC66 | 0.69 |
| MISC67 | 0.59 |
| MISC69 | 0.20 |
There are 2 items with communality < 0.40.
| fanal15.communality | item | |
|---|---|---|
| ATT41 | 0.33 | ATT41 |
| MISC69 | 0.20 | MISC69 |
| PA1 | PA3 | PA12 | PA2 | PA5 | PA6 | PA7 | PA4 | PA9 | PA8 | PA11 | PA13 | PA15 | PA10 | PA14 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| TRAIN01 | -0.09 | 0.22 | 0.03 | -0.05 | -0.09 | -0.05 | 0.01 | 0.01 | 0.01 | 0.46 | 0.04 | 0.04 | 0.01 | 0.12 | -0.14 |
| TRAIN02 | 0.01 | 0.01 | 0.02 | 0.03 | 0.05 | 0.02 | 0.01 | -0.09 | 0.02 | 0.61 | 0.07 | -0.06 | 0.05 | -0.02 | 0.06 |
| TRAIN03 | 0.00 | -0.06 | -0.04 | -0.03 | 0.05 | 0.01 | 0.06 | 0.04 | -0.07 | 0.75 | 0.05 | 0.04 | 0.02 | 0.03 | 0.04 |
| TRAIN04 | 0.08 | 0.33 | -0.03 | -0.01 | -0.03 | 0.04 | 0.03 | -0.04 | 0.02 | 0.48 | -0.07 | -0.04 | 0.13 | 0.02 | -0.21 |
| TRAIN07 | 0.08 | 0.67 | -0.10 | -0.04 | -0.05 | 0.00 | 0.02 | 0.02 | 0.00 | 0.21 | -0.02 | -0.05 | 0.00 | 0.00 | -0.01 |
| AGG09 | 0.21 | 0.04 | 0.74 | 0.01 | 0.05 | -0.05 | -0.05 | 0.01 | -0.01 | 0.04 | 0.01 | 0.07 | 0.05 | -0.07 | 0.02 |
| AGG10 | -0.07 | -0.04 | 0.83 | 0.06 | -0.03 | 0.01 | 0.11 | 0.01 | 0.02 | -0.01 | 0.05 | -0.07 | 0.04 | -0.03 | 0.05 |
| AGG14 | 0.04 | 0.10 | 0.65 | 0.07 | 0.00 | 0.06 | 0.13 | 0.03 | 0.01 | -0.06 | -0.08 | -0.14 | 0.00 | 0.12 | 0.06 |
| AGG15 | 0.28 | 0.00 | 0.73 | -0.07 | 0.02 | 0.01 | -0.06 | 0.10 | -0.09 | -0.01 | 0.08 | 0.09 | -0.03 | 0.04 | -0.12 |
| AGG16 | -0.11 | 0.04 | 0.29 | -0.06 | 0.06 | -0.03 | -0.06 | 0.51 | 0.33 | 0.10 | -0.08 | 0.01 | 0.01 | -0.13 | 0.09 |
| AGG18 | -0.14 | -0.01 | 0.28 | -0.03 | 0.00 | -0.11 | -0.05 | 0.54 | 0.29 | 0.07 | -0.05 | 0.08 | 0.08 | -0.08 | 0.14 |
| AGG19 | 0.06 | 0.03 | 0.00 | 0.07 | 0.02 | 0.08 | 0.03 | 0.86 | -0.02 | 0.00 | 0.06 | 0.01 | -0.08 | 0.00 | -0.05 |
| AGG20 | 0.04 | -0.02 | -0.08 | -0.03 | 0.02 | 0.00 | 0.03 | 0.69 | -0.09 | -0.06 | 0.10 | -0.15 | 0.18 | 0.10 | 0.00 |
| FEAR21 | 0.84 | 0.01 | 0.07 | 0.01 | 0.04 | -0.01 | 0.00 | 0.02 | 0.06 | 0.00 | 0.06 | 0.01 | 0.02 | 0.00 | 0.02 |
| FEAR23 | 0.77 | 0.00 | 0.12 | -0.01 | 0.06 | -0.03 | 0.06 | -0.01 | 0.13 | 0.00 | -0.05 | 0.00 | 0.02 | -0.05 | 0.03 |
| FEAR24 | 0.86 | 0.01 | 0.08 | -0.06 | -0.02 | 0.03 | -0.02 | 0.01 | 0.11 | 0.00 | 0.02 | -0.01 | -0.04 | 0.01 | 0.04 |
| FEAR26 | 0.36 | 0.00 | 0.02 | 0.05 | -0.03 | -0.02 | 0.04 | 0.08 | 0.07 | 0.04 | 0.43 | 0.01 | 0.01 | 0.03 | 0.02 |
| FEAR27 | 0.19 | 0.00 | -0.04 | 0.02 | 0.02 | 0.01 | 0.03 | 0.05 | 0.85 | -0.03 | 0.00 | -0.02 | -0.01 | 0.05 | -0.04 |
| FEAR28 | 0.43 | 0.11 | -0.08 | 0.02 | 0.34 | 0.05 | 0.03 | -0.02 | 0.05 | 0.02 | 0.18 | -0.06 | 0.10 | -0.15 | 0.03 |
| FEAR29 | -0.06 | 0.00 | 0.08 | -0.02 | -0.03 | 0.01 | 0.03 | -0.01 | 0.06 | 0.07 | 0.71 | 0.04 | -0.04 | 0.04 | 0.01 |
| FEAR30 | -0.01 | 0.04 | -0.01 | 0.02 | 0.08 | -0.01 | 0.09 | 0.10 | 0.04 | 0.00 | 0.68 | -0.03 | 0.03 | 0.06 | -0.04 |
| FEAR31 | 0.07 | 0.02 | -0.07 | -0.02 | 0.04 | 0.02 | 0.03 | -0.07 | 0.78 | -0.01 | 0.12 | -0.04 | 0.06 | 0.00 | 0.01 |
| SEPR32 | 0.07 | -0.01 | 0.01 | -0.06 | -0.05 | 0.07 | 0.77 | 0.05 | -0.01 | -0.03 | 0.05 | -0.01 | 0.06 | -0.11 | 0.07 |
| SEPR33 | -0.07 | 0.03 | 0.00 | 0.01 | 0.02 | -0.01 | 0.78 | -0.03 | 0.04 | 0.07 | 0.04 | 0.00 | 0.00 | 0.00 | 0.05 |
| SEPR34 | -0.03 | 0.03 | 0.07 | 0.00 | 0.06 | -0.03 | 0.79 | -0.03 | 0.03 | 0.03 | -0.01 | 0.06 | -0.02 | 0.09 | -0.08 |
| EXCITE35 | 0.14 | 0.02 | -0.05 | -0.08 | -0.07 | 0.55 | 0.13 | 0.04 | -0.01 | 0.08 | -0.06 | 0.11 | -0.04 | 0.03 | 0.16 |
| EXCITE36 | -0.01 | 0.00 | 0.01 | 0.12 | 0.01 | 0.64 | -0.06 | -0.01 | -0.07 | 0.01 | 0.08 | 0.13 | 0.04 | -0.08 | 0.07 |
| EXCITE37 | -0.01 | 0.04 | 0.04 | -0.05 | -0.02 | 0.82 | 0.02 | 0.03 | 0.03 | -0.01 | -0.03 | 0.00 | 0.00 | 0.02 | -0.02 |
| EXCITE38 | -0.04 | -0.08 | 0.00 | 0.04 | 0.05 | 0.79 | -0.02 | 0.01 | 0.04 | -0.01 | 0.00 | -0.02 | 0.06 | 0.02 | -0.04 |
| ATT39 | 0.11 | 0.03 | 0.01 | 0.04 | -0.04 | 0.06 | 0.03 | -0.03 | -0.07 | -0.01 | -0.01 | 0.07 | -0.08 | 0.05 | 0.67 |
| ATT41 | 0.06 | 0.06 | -0.14 | 0.05 | 0.02 | -0.02 | 0.09 | 0.07 | -0.05 | 0.03 | -0.05 | 0.04 | 0.15 | 0.19 | 0.44 |
| PLAY43 | -0.28 | 0.01 | -0.23 | 0.50 | 0.02 | 0.08 | -0.04 | -0.08 | 0.11 | -0.06 | -0.01 | 0.07 | 0.00 | 0.04 | -0.02 |
| PLAY44 | 0.02 | 0.04 | -0.04 | 0.88 | -0.02 | 0.03 | -0.02 | 0.11 | -0.01 | 0.01 | 0.03 | 0.02 | 0.03 | -0.07 | 0.00 |
| PLAY45 | 0.01 | -0.02 | 0.04 | 0.83 | -0.03 | -0.03 | -0.06 | -0.07 | 0.06 | -0.05 | 0.01 | 0.07 | 0.03 | -0.01 | 0.08 |
| PLAY46 | 0.00 | -0.10 | 0.11 | 0.80 | 0.02 | 0.02 | 0.05 | -0.01 | -0.07 | 0.02 | -0.05 | -0.01 | 0.00 | 0.01 | -0.05 |
| IMP47 | 0.04 | -0.04 | 0.03 | 0.15 | -0.02 | 0.07 | -0.01 | 0.01 | 0.04 | 0.16 | -0.04 | 0.08 | 0.58 | 0.14 | -0.05 |
| IMP48 | -0.08 | -0.01 | 0.07 | 0.02 | -0.02 | 0.10 | 0.04 | 0.00 | 0.03 | 0.04 | 0.03 | 0.00 | 0.72 | 0.03 | 0.00 |
| MISC52 | -0.06 | 0.05 | 0.11 | -0.10 | 0.04 | 0.05 | -0.08 | -0.09 | 0.10 | -0.02 | 0.10 | -0.02 | 0.05 | 0.61 | 0.14 |
| MISC53 | 0.02 | -0.01 | -0.03 | -0.03 | 0.01 | -0.01 | 0.02 | 0.06 | 0.00 | 0.07 | 0.03 | 0.00 | 0.05 | 0.74 | -0.01 |
| MISC54 | -0.02 | 0.16 | -0.01 | -0.04 | 0.67 | 0.06 | -0.04 | -0.03 | 0.01 | 0.01 | 0.11 | -0.10 | 0.05 | 0.02 | 0.07 |
| MISC55 | 0.02 | -0.05 | -0.02 | 0.05 | 0.91 | -0.01 | 0.06 | 0.05 | 0.00 | 0.04 | -0.05 | 0.01 | -0.08 | 0.00 | -0.01 |
| MISC56 | -0.05 | 0.01 | 0.05 | -0.10 | 0.74 | -0.01 | -0.04 | -0.03 | 0.03 | -0.02 | 0.03 | 0.08 | 0.07 | 0.02 | -0.05 |
| MISC59 | 0.08 | 0.10 | -0.09 | 0.04 | -0.01 | -0.04 | 0.28 | 0.10 | -0.08 | -0.07 | 0.01 | 0.36 | 0.39 | 0.08 | -0.08 |
| MISC60 | -0.04 | -0.01 | -0.05 | 0.02 | 0.04 | 0.06 | -0.01 | -0.11 | 0.02 | 0.04 | 0.04 | 0.72 | 0.04 | 0.01 | 0.07 |
| MISC61 | 0.04 | -0.02 | 0.02 | 0.14 | -0.04 | 0.10 | 0.11 | 0.03 | -0.09 | -0.04 | -0.04 | 0.68 | 0.01 | -0.03 | 0.02 |
| MISC62 | -0.11 | 0.39 | 0.06 | -0.08 | -0.01 | 0.03 | -0.04 | 0.17 | 0.30 | 0.03 | 0.00 | 0.22 | 0.03 | 0.00 | 0.03 |
| MISC64 | -0.08 | 0.80 | 0.05 | 0.02 | 0.01 | -0.02 | 0.04 | 0.00 | -0.03 | -0.02 | 0.01 | 0.01 | -0.09 | 0.04 | 0.02 |
| MISC65 | -0.09 | 0.75 | 0.03 | -0.02 | -0.01 | 0.00 | 0.02 | 0.06 | 0.06 | 0.03 | 0.03 | 0.02 | 0.00 | 0.07 | -0.01 |
| MISC66 | 0.18 | 0.62 | 0.00 | -0.07 | 0.17 | -0.04 | 0.03 | -0.08 | -0.02 | 0.00 | 0.07 | -0.04 | 0.14 | -0.06 | 0.02 |
| MISC67 | 0.15 | 0.57 | 0.01 | -0.13 | 0.13 | -0.02 | 0.02 | -0.03 | 0.00 | -0.07 | 0.06 | -0.01 | 0.14 | -0.08 | 0.08 |
| MISC69 | 0.10 | 0.12 | -0.01 | 0.02 | 0.24 | 0.02 | 0.13 | 0.08 | 0.10 | 0.00 | -0.24 | 0.05 | 0.01 | 0.18 | -0.02 |
| largest | maximum | itemNames | itemDescriptions | |
|---|---|---|---|---|
| 15 | PA1 | 0.84 | FEAR21 | When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel |
| 16 | PA1 | 0.77 | FEAR23 | When an unfamiliar person visits your home or approaches the dog when in his/her home kennel |
| 17 | PA1 | 0.86 | FEAR24 | When an unfamiliar person tries to touch or pet the dog |
| 20 | PA1 | 0.43 | FEAR28 | When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.) |
| 26 | PA10 | 0.61 | MISC52 | Begs persistently for food when people are eating |
| 27 | PA10 | 0.74 | MISC53 | Steals food |
| 18 | PA11 | 0.43 | FEAR26 | When examined/treated by a veterinarian |
| 21 | PA11 | 0.71 | FEAR29 | When having nails trimmed, or feet touched/handled |
| 22 | PA11 | 0.68 | FEAR30 | When groomed or bathed |
| 1 | PA12 | 0.74 | AGG09 | Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash |
| 2 | PA12 | 0.83 | AGG10 | Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel |
| 3 | PA12 | 0.65 | AGG14 | When strangers walk past when the dog is in his/her home run or kennel |
| 4 | PA12 | 0.73 | AGG15 | When an unfamiliar person tries to touch or pet the dog |
| 32 | PA13 | 0.72 | MISC60 | Playful, puppyish, boisterous |
| 33 | PA13 | 0.68 | MISC61 | Active, energetic, always on the go |
| 9 | PA14 | 0.67 | ATT39 | Displays a strong attachment for you or another familiar person |
| 10 | PA14 | 0.44 | ATT41 | Tends to nudge or paw you (or others) for attention |
| 24 | PA15 | 0.58 | IMP47 | Impulsive; doesn’t seem to think before s/he acts |
| 25 | PA15 | 0.72 | IMP48 | Becomes frustrated/impatient in a wide range of situations |
| 31 | PA15 | 0.39 | MISC59 | Hyperactive, restless, has trouble settling down |
| 40 | PA2 | 0.50 | PLAY43 | Eagerly engages in play with new/unfamiliar people |
| 41 | PA2 | 0.88 | PLAY44 | Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person |
| 42 | PA2 | 0.83 | PLAY45 | Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown |
| 43 | PA2 | 0.80 | PLAY46 | Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task |
| 34 | PA3 | 0.39 | MISC62 | Becomes highly excited and/or distracted when encountering unfamiliar dogs |
| 35 | PA3 | 0.80 | MISC64 | When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects |
| 36 | PA3 | 0.75 | MISC65 | Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.) |
| 37 | PA3 | 0.62 | MISC66 | Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work |
| 38 | PA3 | 0.57 | MISC67 | Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work |
| 51 | PA3 | 0.67 | TRAIN07 | Unfocused; is easily distracted by interesting sights, sounds or smells |
| 5 | PA4 | 0.51 | AGG16 | When approached directly by an unfamiliar dog while being walked/exercised on a leash |
| 6 | PA4 | 0.54 | AGG18 | When barked, growled, or lunged at by another dog |
| 7 | PA4 | 0.86 | AGG19 | Towards other familiar dogs |
| 8 | PA4 | 0.69 | AGG20 | When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog |
| 28 | PA5 | 0.67 | MISC54 | Reluctant to/nervous about crossing grates or other unfamiliar surfaces |
| 29 | PA5 | 0.91 | MISC55 | Reluctant to/nervous about crossing shiny or slippery floors |
| 30 | PA5 | 0.74 | MISC56 | Nervous or frightened when ascending or descending some types of stairs |
| 39 | PA5 | 0.24 | MISC69 | Chases/follows shadows, light spots, etc. |
| 11 | PA6 | 0.55 | EXCITE35 | Excitable when you first arrive home, or at the dog’s kennel, after a brief absence |
| 12 | PA6 | 0.64 | EXCITE36 | Excitable when playing with you or other familiar persons |
| 13 | PA6 | 0.82 | EXCITE37 | Excitable just before being taken out for a walk |
| 14 | PA6 | 0.79 | EXCITE38 | Excitable just before being taken out for work or training |
| 44 | PA7 | 0.77 | SEPR32 | Restlessness/agitation/pacing when left alone |
| 45 | PA7 | 0.78 | SEPR33 | Barking or whining when left alone |
| 46 | PA7 | 0.79 | SEPR34 | Chewing/scratching at doors, floor, fencing, etc., when left alone |
| 47 | PA8 | 0.46 | TRAIN01 | Is hard to recall when off the leash |
| 48 | PA8 | 0.61 | TRAIN02 | Is slow to obey a ‘sit’ command |
| 49 | PA8 | 0.75 | TRAIN03 | Is slow to obey a ‘stay’ command |
| 50 | PA8 | 0.48 | TRAIN04 | Has difficulty attending/listening to things you say or do |
| 19 | PA9 | 0.85 | FEAR27 | When approached directly by an unfamiliar dog |
| 23 | PA9 | 0.78 | FEAR31 | When barked, growled, or lunged at by an unfamiliar dog |
| PA1 | PA3 | PA12 | PA2 | PA5 | PA6 | PA7 | PA4 | PA9 | PA8 | PA11 | PA13 | PA15 | PA10 | PA14 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| alpha | 0.836 | 0.786 | 0.76 | 0.812 | 0.625 | 0.787 | 0.735 | 0.752 | 0.803 | 0.693 | 0.615 | 0.71 | 0.683 | 0.623 | 0.439 |
omega is thought to be better measure of reliability than alpha, because it looks at the relationships between all the items rather than just the ones within each factor. It’s different than alpha because it assumes that there is a genral factor, g, that all items have in common. This is listed as the first row of the table below.
There are three omegas for each factor:
From EFAtools::OMEGA documentation:
Omegas refer to the correlation between a factor and a unit-weighted composite score and thus the true score variance in a unit-weighted composite based on the respective indicators. Omega total is the total true score variance in a composite. Omega hierarchical is the true score variance in a composite that is attributable to the general factor, and omega subscale is the true score variance in a composite attributable to all subscales / group factors (for the whole scale) or to the specific subscale / group factor (for subscale composites).
Interpretation of omega_subscale
no universal guideline
0.50 is minimum, 0.75 preferable (watkins books,rodrigues16, zimbarg2005
## Omega total, omega hierarchical, omega subscale, H index, explained common variance (ECV), and percent of uncontaminated correlations (PUC) for the general factor (top row) and omegas and H index for the group factors:
##
## tot hier sub H ECV PUC
## g 0.944 0.574 0.199 0.877 0.221 0.945
## F1 0.828 0.272 0.555 0.802
## F2 0.644 0.070 0.574 0.630
## F3 0.717 0.264 0.453 0.587
## F4 0.815 0.130 0.685 0.808
## F5 0.555 0.032 0.522 0.675
## F6 0.488 0.028 0.460 0.510
## F7 0.564 0.141 0.423 0.518
## F8 0.816 0.053 0.763 0.873
## F9 0.841 0.366 0.475 0.727
## F10 0.723 0.164 0.559 0.767
## F11 0.799 0.209 0.590 0.780
## F12 0.765 0.027 0.738 0.820
## F13 0.841 0.167 0.674 0.760
## F14 0.660 0.170 0.490 0.654
## F15 0.831 0.224 0.607 0.707
include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.
Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (201 0)
This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.
## Warning in polychoric(ddNum16, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1240 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.
The chi-squared for the Bartlett test is 3.917561^{4} with 1431 DF, p = 0e+00.
From EFAtools::KMO documentation:
The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis
The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.
## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.
[1] 0.850597
## Warning in polychoric(imputedNumericDF16, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1240 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.
The chi-squared for the Bartlett test is 3.7685238^{4} with 1431 DF, p = 0e+00.
From EFAtools::KMO documentation:
The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis
The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.
## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.
[1] 0.850597
For factor analysis, it is recommended that some of the item
correlationsshould be between 0.3 and 0.9. Polychoric correlations were
computed using the polychoric function in the
psych package in R with options smooth = TRUE
to adjust for non-positive-definite matrices and
correct = 0.01 to avoid computation problems with
covariance of zero.
The minimum correlation in this data set is -0.477. The maximum correlation in this data set is 0.856.
#### Post-Imputation
The post imputation polyserial correlation was also computed using
the polychoric function, with no setting
smooth = TRUE and correct = 0.01.
The minimum correlation was -0.466. The maximum correlation was 0.851.
From the EFAtools documentation:
Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.
Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not
PCA) - fm = “wls” (weighted least squares because pa gave errors and
weighted recommended for ordinal data. - use = “all.obs” (since we have
imputed missing values, we can use all data points) - cor = “poly” (use
polychoric correlation matrix) - n.iter = 100 (run for 100
iterations)
The suggested number of factors is 12.
MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.
| Number of Factors | MAP value |
|---|---|
| 1 | 0.0284 |
| 2 | 0.0243 |
| 3 | 0.0190 |
| 4 | 0.0166 |
| 5 | 0.0151 |
| 6 | 0.0146 |
| 7 | 0.0145 |
| 8 | 0.0136 |
| 9 | 0.0133 |
| 10 | 0.0131 |
| 11 | 0.0127 |
| 12 | 0.0127 |
| 13 | 0.0131 |
| 14 | 0.0131 |
| 15 | 0.0137 |
| 16 | 0.0144 |
| 17 | 0.0151 |
| 18 | 0.0157 |
## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1240 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.
Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.7249164. Should be > 0.9; need reference)
| fanal16.communality | |
|---|---|
| TRAIN01 | 0.51 |
| TRAIN02 | 0.45 |
| TRAIN03 | 0.61 |
| TRAIN04 | 0.60 |
| TRAIN07 | 0.63 |
| AGG09 | 0.77 |
| AGG10 | 0.69 |
| AGG14 | 0.52 |
| AGG15 | 0.80 |
| AGG16 | 0.76 |
| AGG18 | 0.74 |
| AGG19 | 0.79 |
| AGG20 | 0.52 |
| FEAR21 | 0.84 |
| FEAR22 | 0.41 |
| FEAR23 | 0.81 |
| FEAR24 | 0.87 |
| FEAR25 | 0.52 |
| FEAR26 | 0.44 |
| FEAR27 | 0.86 |
| FEAR28 | 0.67 |
| FEAR29 | 0.65 |
| FEAR30 | 0.61 |
| FEAR31 | 0.68 |
| SEPR32 | 0.69 |
| SEPR33 | 0.66 |
| SEPR34 | 0.70 |
| EXCITE35 | 0.48 |
| EXCITE36 | 0.57 |
| EXCITE37 | 0.66 |
| EXCITE38 | 0.66 |
| ATT39 | 0.41 |
| ATT41 | 0.37 |
| PLAY43 | 0.55 |
| PLAY44 | 0.81 |
| PLAY45 | 0.78 |
| PLAY46 | 0.73 |
| IMP47 | 0.62 |
| IMP48 | 0.62 |
| MISC51 | 0.49 |
| MISC52 | 0.63 |
| MISC53 | 0.56 |
| MISC54 | 0.63 |
| MISC55 | 0.75 |
| MISC56 | 0.63 |
| MISC59 | 0.57 |
| MISC60 | 0.57 |
| MISC61 | 0.68 |
| MISC62 | 0.45 |
| MISC64 | 0.59 |
| MISC65 | 0.65 |
| MISC66 | 0.70 |
| MISC67 | 0.63 |
| MISC69 | 0.38 |
There are 2 items with communality < 0.40.
| fanal16.communality | item | |
|---|---|---|
| ATT41 | 0.37 | ATT41 |
| MISC69 | 0.38 | MISC69 |
| PA9 | PA1 | PA3 | PA2 | PA5 | PA7 | PA6 | PA4 | PA12 | PA8 | PA15 | PA11 | PA13 | PA10 | PA14 | PA16 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| TRAIN01 | -0.03 | 0.20 | -0.01 | -0.02 | -0.10 | -0.01 | -0.06 | 0.05 | -0.01 | 0.43 | -0.03 | 0.06 | 0.04 | 0.14 | -0.21 | 0.19 |
| TRAIN02 | -0.02 | 0.01 | 0.05 | 0.02 | 0.05 | 0.02 | 0.02 | -0.09 | 0.04 | 0.64 | 0.05 | 0.03 | -0.04 | 0.01 | 0.05 | -0.11 |
| TRAIN03 | -0.01 | -0.06 | -0.03 | -0.03 | 0.04 | 0.06 | 0.01 | 0.05 | -0.07 | 0.76 | 0.02 | 0.02 | 0.05 | 0.05 | 0.03 | -0.03 |
| TRAIN04 | 0.05 | 0.31 | -0.02 | -0.04 | -0.04 | 0.00 | 0.04 | -0.07 | 0.02 | 0.45 | 0.18 | -0.01 | -0.07 | -0.06 | -0.17 | 0.14 |
| TRAIN07 | 0.05 | 0.64 | -0.08 | -0.07 | -0.08 | 0.01 | 0.00 | -0.01 | 0.00 | 0.20 | 0.02 | 0.04 | -0.05 | -0.04 | 0.02 | 0.10 |
| AGG09 | 0.24 | 0.05 | 0.73 | 0.01 | 0.06 | -0.06 | -0.04 | 0.02 | -0.02 | 0.02 | 0.05 | 0.06 | 0.07 | -0.08 | 0.01 | 0.08 |
| AGG10 | -0.05 | -0.02 | 0.80 | 0.08 | -0.01 | 0.13 | 0.00 | 0.06 | 0.01 | 0.00 | 0.02 | 0.02 | -0.07 | 0.01 | 0.05 | -0.07 |
| AGG14 | 0.05 | 0.08 | 0.64 | 0.06 | -0.01 | 0.11 | 0.06 | 0.04 | -0.02 | -0.06 | 0.02 | -0.02 | -0.16 | 0.08 | 0.12 | 0.13 |
| AGG15 | 0.27 | 0.01 | 0.72 | -0.05 | 0.05 | -0.04 | 0.00 | 0.13 | -0.08 | 0.00 | -0.01 | 0.04 | 0.07 | 0.06 | -0.14 | -0.09 |
| AGG16 | -0.12 | 0.05 | 0.30 | -0.06 | 0.06 | -0.06 | -0.02 | 0.51 | 0.33 | 0.10 | 0.00 | -0.06 | 0.01 | -0.12 | 0.11 | 0.04 |
| AGG18 | -0.13 | -0.01 | 0.27 | -0.03 | -0.01 | -0.04 | -0.10 | 0.55 | 0.28 | 0.06 | 0.07 | -0.02 | 0.09 | -0.07 | 0.14 | 0.06 |
| AGG19 | 0.04 | 0.01 | 0.01 | 0.07 | 0.00 | 0.03 | 0.09 | 0.86 | 0.00 | 0.00 | -0.07 | 0.05 | 0.03 | 0.00 | -0.07 | 0.00 |
| AGG20 | 0.01 | -0.05 | -0.05 | -0.05 | -0.01 | 0.02 | -0.01 | 0.67 | -0.08 | -0.06 | 0.19 | 0.09 | -0.15 | 0.08 | 0.02 | -0.02 |
| FEAR21 | 0.82 | -0.01 | 0.11 | -0.03 | 0.01 | -0.01 | 0.01 | -0.01 | 0.08 | -0.02 | 0.02 | 0.10 | 0.03 | -0.03 | 0.01 | 0.04 |
| FEAR22 | 0.36 | 0.16 | -0.27 | 0.01 | 0.20 | 0.04 | 0.01 | 0.22 | -0.09 | 0.06 | -0.03 | 0.00 | -0.14 | 0.08 | 0.16 | -0.06 |
| FEAR23 | 0.77 | -0.01 | 0.15 | -0.03 | 0.04 | 0.06 | -0.02 | -0.01 | 0.15 | 0.00 | 0.01 | -0.04 | 0.01 | -0.05 | 0.03 | 0.01 |
| FEAR24 | 0.81 | 0.00 | 0.13 | -0.09 | -0.04 | -0.01 | 0.04 | -0.02 | 0.16 | 0.00 | -0.03 | 0.03 | 0.02 | 0.00 | 0.02 | -0.06 |
| FEAR25 | 0.41 | 0.20 | -0.15 | 0.08 | 0.26 | 0.03 | 0.00 | 0.12 | -0.01 | 0.06 | 0.06 | 0.00 | -0.15 | 0.05 | 0.14 | 0.14 |
| FEAR26 | 0.35 | 0.00 | 0.02 | 0.06 | -0.02 | 0.06 | -0.02 | 0.08 | 0.09 | 0.04 | 0.01 | 0.37 | 0.01 | 0.06 | -0.02 | -0.14 |
| FEAR27 | 0.16 | 0.00 | -0.04 | 0.02 | 0.03 | 0.03 | 0.01 | 0.04 | 0.86 | -0.02 | 0.01 | 0.02 | -0.03 | 0.04 | -0.02 | 0.02 |
| FEAR28 | 0.49 | 0.13 | -0.10 | 0.06 | 0.34 | 0.05 | 0.04 | 0.03 | 0.04 | 0.05 | 0.04 | 0.12 | -0.08 | -0.07 | 0.03 | -0.10 |
| FEAR29 | -0.05 | -0.01 | 0.05 | -0.03 | -0.03 | -0.01 | 0.01 | -0.03 | 0.02 | 0.02 | -0.02 | 0.83 | 0.03 | -0.01 | 0.02 | 0.04 |
| FEAR30 | 0.00 | 0.03 | -0.04 | 0.02 | 0.10 | 0.07 | -0.02 | 0.10 | 0.01 | -0.02 | 0.05 | 0.67 | -0.05 | 0.04 | -0.01 | -0.05 |
| FEAR31 | 0.10 | 0.04 | -0.11 | 0.01 | 0.05 | 0.03 | 0.01 | -0.02 | 0.75 | 0.00 | 0.03 | 0.09 | -0.05 | 0.06 | 0.00 | -0.03 |
| SEPR32 | 0.05 | 0.00 | 0.03 | -0.06 | -0.05 | 0.79 | 0.07 | 0.04 | 0.01 | -0.02 | 0.04 | 0.03 | 0.01 | -0.09 | 0.05 | -0.09 |
| SEPR33 | -0.08 | 0.02 | 0.00 | 0.02 | 0.02 | 0.79 | -0.01 | -0.03 | 0.05 | 0.08 | 0.00 | 0.02 | -0.01 | 0.01 | 0.05 | -0.04 |
| SEPR34 | -0.02 | 0.01 | 0.04 | 0.01 | 0.05 | 0.79 | -0.03 | -0.03 | 0.01 | 0.01 | -0.01 | 0.02 | 0.03 | 0.05 | -0.08 | 0.14 |
| EXCITE35 | 0.11 | 0.01 | -0.02 | -0.09 | -0.09 | 0.13 | 0.57 | 0.02 | 0.01 | 0.08 | -0.04 | -0.05 | 0.14 | 0.04 | 0.12 | -0.01 |
| EXCITE36 | 0.01 | 0.02 | 0.00 | 0.15 | 0.03 | -0.05 | 0.64 | 0.01 | -0.07 | 0.02 | 0.03 | 0.04 | 0.13 | -0.03 | 0.03 | -0.07 |
| EXCITE37 | -0.04 | 0.03 | 0.05 | -0.06 | -0.02 | 0.02 | 0.83 | 0.00 | 0.04 | -0.02 | 0.01 | -0.01 | 0.00 | 0.00 | -0.04 | 0.01 |
| EXCITE38 | -0.01 | -0.08 | -0.03 | 0.06 | 0.06 | -0.03 | 0.77 | 0.03 | 0.01 | 0.00 | 0.07 | 0.01 | -0.07 | 0.01 | 0.00 | 0.05 |
| ATT39 | 0.06 | 0.03 | 0.09 | -0.01 | -0.09 | 0.05 | 0.11 | -0.08 | -0.03 | -0.04 | -0.11 | 0.03 | 0.17 | 0.07 | 0.54 | -0.02 |
| ATT41 | 0.05 | 0.03 | -0.11 | 0.00 | -0.05 | 0.07 | -0.01 | 0.03 | -0.08 | 0.00 | 0.14 | 0.05 | 0.09 | 0.16 | 0.47 | 0.17 |
| PLAY43 | -0.28 | 0.00 | -0.25 | 0.51 | 0.03 | -0.04 | 0.07 | -0.07 | 0.08 | -0.05 | 0.02 | -0.02 | 0.05 | 0.03 | 0.01 | 0.01 |
| PLAY44 | -0.02 | 0.02 | -0.01 | 0.84 | -0.04 | -0.01 | 0.05 | 0.08 | 0.01 | 0.00 | 0.05 | 0.04 | 0.04 | -0.10 | -0.02 | 0.00 |
| PLAY45 | 0.01 | -0.01 | 0.05 | 0.84 | -0.04 | -0.04 | -0.03 | -0.06 | 0.07 | -0.03 | 0.01 | -0.03 | 0.08 | 0.02 | 0.06 | -0.07 |
| PLAY46 | 0.02 | -0.11 | 0.11 | 0.81 | 0.01 | 0.05 | 0.02 | 0.01 | -0.08 | 0.02 | -0.01 | -0.04 | -0.02 | 0.00 | -0.05 | 0.06 |
| IMP47 | 0.03 | -0.06 | 0.04 | 0.09 | -0.04 | -0.04 | 0.07 | -0.03 | 0.03 | 0.10 | 0.65 | 0.04 | 0.06 | 0.06 | -0.03 | 0.14 |
| IMP48 | -0.08 | 0.02 | 0.06 | 0.00 | -0.01 | 0.04 | 0.08 | 0.00 | 0.04 | 0.04 | 0.73 | 0.01 | -0.02 | 0.04 | 0.02 | -0.08 |
| MISC51 | 0.02 | 0.11 | -0.01 | -0.06 | -0.03 | 0.23 | 0.04 | 0.15 | -0.05 | 0.04 | 0.05 | -0.05 | 0.12 | 0.27 | -0.27 | 0.29 |
| MISC52 | -0.03 | 0.04 | 0.08 | -0.02 | 0.03 | -0.06 | 0.02 | -0.03 | 0.08 | 0.02 | 0.00 | 0.01 | -0.03 | 0.76 | 0.11 | -0.07 |
| MISC53 | -0.04 | -0.06 | -0.02 | -0.05 | -0.02 | 0.03 | -0.01 | 0.03 | 0.02 | 0.05 | 0.07 | 0.04 | 0.02 | 0.68 | -0.08 | 0.07 |
| MISC54 | -0.01 | 0.16 | 0.00 | -0.04 | 0.65 | -0.02 | 0.06 | -0.02 | 0.01 | 0.02 | 0.01 | 0.11 | -0.09 | 0.06 | 0.05 | 0.01 |
| MISC55 | 0.00 | -0.07 | 0.01 | 0.02 | 0.87 | 0.05 | 0.00 | 0.03 | 0.00 | 0.04 | -0.06 | 0.01 | 0.00 | -0.04 | 0.02 | 0.07 |
| MISC56 | -0.08 | 0.02 | 0.07 | -0.09 | 0.78 | -0.02 | -0.01 | -0.04 | 0.06 | -0.02 | 0.06 | 0.01 | 0.10 | 0.05 | -0.10 | -0.05 |
| MISC59 | 0.07 | 0.10 | -0.09 | 0.04 | 0.00 | 0.27 | -0.04 | 0.09 | -0.08 | -0.06 | 0.43 | 0.02 | 0.32 | 0.03 | -0.05 | 0.00 |
| MISC60 | 0.00 | 0.01 | -0.08 | 0.08 | 0.07 | -0.01 | 0.07 | -0.09 | -0.01 | 0.04 | 0.08 | 0.04 | 0.66 | 0.01 | 0.09 | 0.03 |
| MISC61 | 0.07 | -0.01 | -0.02 | 0.20 | -0.01 | 0.12 | 0.11 | 0.06 | -0.11 | -0.02 | 0.03 | -0.07 | 0.63 | -0.03 | 0.03 | -0.01 |
| MISC62 | -0.10 | 0.39 | 0.03 | -0.04 | 0.00 | -0.03 | 0.03 | 0.19 | 0.30 | 0.04 | 0.03 | -0.01 | 0.21 | 0.03 | 0.03 | 0.02 |
| MISC64 | -0.13 | 0.77 | 0.08 | -0.01 | 0.00 | 0.04 | -0.01 | -0.04 | 0.00 | -0.02 | -0.06 | 0.05 | 0.03 | 0.01 | 0.01 | 0.04 |
| MISC65 | -0.11 | 0.73 | 0.04 | -0.03 | -0.03 | 0.02 | 0.00 | 0.04 | 0.06 | 0.03 | 0.01 | 0.05 | 0.02 | 0.06 | -0.01 | 0.07 |
| MISC66 | 0.19 | 0.64 | 0.00 | -0.04 | 0.16 | 0.06 | -0.04 | -0.05 | 0.00 | 0.02 | 0.09 | 0.01 | -0.03 | 0.02 | -0.03 | -0.09 |
| MISC67 | 0.18 | 0.61 | 0.00 | -0.10 | 0.13 | 0.06 | -0.03 | 0.03 | 0.00 | -0.03 | 0.08 | -0.03 | 0.00 | 0.03 | 0.06 | -0.17 |
| MISC69 | 0.09 | 0.04 | 0.00 | -0.06 | 0.21 | 0.05 | 0.04 | -0.02 | 0.05 | -0.07 | 0.09 | -0.03 | 0.01 | -0.01 | 0.11 | 0.51 |
| largest | maximum | itemNames | itemDescriptions | |
|---|---|---|---|---|
| 37 | PA1 | 0.39 | MISC62 | Becomes highly excited and/or distracted when encountering unfamiliar dogs |
| 38 | PA1 | 0.77 | MISC64 | When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects |
| 39 | PA1 | 0.73 | MISC65 | Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.) |
| 40 | PA1 | 0.64 | MISC66 | Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work |
| 41 | PA1 | 0.61 | MISC67 | Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work |
| 54 | PA1 | 0.64 | TRAIN07 | Unfocused; is easily distracted by interesting sights, sounds or smells |
| 29 | PA10 | 0.76 | MISC52 | Begs persistently for food when people are eating |
| 30 | PA10 | 0.68 | MISC53 | Steals food |
| 20 | PA11 | 0.37 | FEAR26 | When examined/treated by a veterinarian |
| 23 | PA11 | 0.83 | FEAR29 | When having nails trimmed, or feet touched/handled |
| 24 | PA11 | 0.67 | FEAR30 | When groomed or bathed |
| 21 | PA12 | 0.86 | FEAR27 | When approached directly by an unfamiliar dog |
| 25 | PA12 | 0.75 | FEAR31 | When barked, growled, or lunged at by an unfamiliar dog |
| 35 | PA13 | 0.66 | MISC60 | Playful, puppyish, boisterous |
| 36 | PA13 | 0.63 | MISC61 | Active, energetic, always on the go |
| 9 | PA14 | 0.54 | ATT39 | Displays a strong attachment for you or another familiar person |
| 10 | PA14 | 0.47 | ATT41 | Tends to nudge or paw you (or others) for attention |
| 26 | PA15 | 0.65 | IMP47 | Impulsive; doesn’t seem to think before s/he acts |
| 27 | PA15 | 0.73 | IMP48 | Becomes frustrated/impatient in a wide range of situations |
| 34 | PA15 | 0.43 | MISC59 | Hyperactive, restless, has trouble settling down |
| 28 | PA16 | 0.29 | MISC51 | Escapes or would escape from home, yard or kennel given the chance |
| 42 | PA16 | 0.51 | MISC69 | Chases/follows shadows, light spots, etc. |
| 43 | PA2 | 0.51 | PLAY43 | Eagerly engages in play with new/unfamiliar people |
| 44 | PA2 | 0.84 | PLAY44 | Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person |
| 45 | PA2 | 0.84 | PLAY45 | Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown |
| 46 | PA2 | 0.81 | PLAY46 | Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task |
| 1 | PA3 | 0.73 | AGG09 | Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash |
| 2 | PA3 | 0.80 | AGG10 | Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel |
| 3 | PA3 | 0.64 | AGG14 | When strangers walk past when the dog is in his/her home run or kennel |
| 4 | PA3 | 0.72 | AGG15 | When an unfamiliar person tries to touch or pet the dog |
| 5 | PA4 | 0.51 | AGG16 | When approached directly by an unfamiliar dog while being walked/exercised on a leash |
| 6 | PA4 | 0.55 | AGG18 | When barked, growled, or lunged at by another dog |
| 7 | PA4 | 0.86 | AGG19 | Towards other familiar dogs |
| 8 | PA4 | 0.67 | AGG20 | When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog |
| 31 | PA5 | 0.65 | MISC54 | Reluctant to/nervous about crossing grates or other unfamiliar surfaces |
| 32 | PA5 | 0.87 | MISC55 | Reluctant to/nervous about crossing shiny or slippery floors |
| 33 | PA5 | 0.78 | MISC56 | Nervous or frightened when ascending or descending some types of stairs |
| 11 | PA6 | 0.57 | EXCITE35 | Excitable when you first arrive home, or at the dog’s kennel, after a brief absence |
| 12 | PA6 | 0.64 | EXCITE36 | Excitable when playing with you or other familiar persons |
| 13 | PA6 | 0.83 | EXCITE37 | Excitable just before being taken out for a walk |
| 14 | PA6 | 0.77 | EXCITE38 | Excitable just before being taken out for work or training |
| 47 | PA7 | 0.79 | SEPR32 | Restlessness/agitation/pacing when left alone |
| 48 | PA7 | 0.79 | SEPR33 | Barking or whining when left alone |
| 49 | PA7 | 0.79 | SEPR34 | Chewing/scratching at doors, floor, fencing, etc., when left alone |
| 50 | PA8 | 0.43 | TRAIN01 | Is hard to recall when off the leash |
| 51 | PA8 | 0.64 | TRAIN02 | Is slow to obey a ‘sit’ command |
| 52 | PA8 | 0.76 | TRAIN03 | Is slow to obey a ‘stay’ command |
| 53 | PA8 | 0.45 | TRAIN04 | Has difficulty attending/listening to things you say or do |
| 15 | PA9 | 0.82 | FEAR21 | When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel |
| 16 | PA9 | 0.36 | FEAR22 | In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.) |
| 17 | PA9 | 0.77 | FEAR23 | When an unfamiliar person visits your home or approaches the dog when in his/her home kennel |
| 18 | PA9 | 0.81 | FEAR24 | When an unfamiliar person tries to touch or pet the dog |
| 19 | PA9 | 0.41 | FEAR25 | In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc. |
| 22 | PA9 | 0.49 | FEAR28 | When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.) |
| PA9 | PA1 | PA3 | PA2 | PA5 | PA7 | PA6 | PA4 | PA12 | PA8 | PA15 | PA11 | PA13 | PA10 | PA14 | PA16 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| alpha | 0.777 | 0.786 | 0.76 | 0.812 | 0.718 | 0.735 | 0.787 | 0.753 | 0.802 | 0.693 | 0.683 | 0.613 | 0.71 | 0.622 | 0.439 | 0.159 |
omega is thought to be better measure of reliability than alpha, because it looks at the relationships between all the items rather than just the ones within each factor. It’s different than alpha because it assumes that there is a genral factor, g, that all items have in common. This is listed as the first row of the table below.
There are three omegas for each factor:
From EFAtools::OMEGA documentation:
Omegas refer to the correlation between a factor and a unit-weighted composite score and thus the true score variance in a unit-weighted composite based on the respective indicators. Omega total is the total true score variance in a composite. Omega hierarchical is the true score variance in a composite that is attributable to the general factor, and omega subscale is the true score variance in a composite attributable to all subscales / group factors (for the whole scale) or to the specific subscale / group factor (for subscale composites).
Interpretation of omega_subscale
no universal guideline
0.50 is minimum, 0.75 preferable (watkins books,rodrigues16, zimbarg2005
## Omega total, omega hierarchical, omega subscale, H index, explained common variance (ECV), and percent of uncontaminated correlations (PUC) for the general factor (top row) and omegas and H index for the group factors:
##
## tot hier sub H ECV PUC
## g 0.948 0.590 0.184 0.884 0.23 0.946
## F1 0.847 0.389 0.458 0.710
## F2 0.701 0.090 0.611 0.648
## F3 0.720 0.267 0.454 0.631
## F4 0.820 0.199 0.621 0.726
## F5 0.521 0.003 0.518 0.590
## F6 0.410 0.028 0.381 0.408
## F7 0.630 0.188 0.442 0.591
## F8 0.403 0.138 0.265 0.305
## F9 0.811 0.055 0.756 0.862
## F10 0.797 0.105 0.692 0.809
## F11 0.701 0.151 0.549 0.761
## F12 0.840 0.185 0.655 0.769
## F13 0.773 0.030 0.743 0.823
## F14 0.855 0.181 0.673 0.759
## F15 0.673 0.205 0.468 0.647
## F16 0.809 0.292 0.517 0.804
include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.
Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (201 0)
This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.
## Warning in polychoric(ddNum17, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1322 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.
The chi-squared for the Bartlett test is 4.0773023^{4} with 1540 DF, p = 0e+00.
From EFAtools::KMO documentation:
The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis
The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.
## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.
[1] 0.8532378
## Warning in polychoric(imputedNumericDF17, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1321 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.
The chi-squared for the Bartlett test is 3.9253542^{4} with 1540 DF, p = 0e+00.
From EFAtools::KMO documentation:
The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis
The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.
## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.
[1] 0.8532378
For factor analysis, it is recommended that some of the item
correlationsshould be between 0.3 and 0.9. Polychoric correlations were
computed using the polychoric function in the
psych package in R with options smooth = TRUE
to adjust for non-positive-definite matrices and
correct = 0.01 to avoid computation problems with
covariance of zero.
The minimum correlation in this data set is -0.477. The maximum correlation in this data set is 0.856.
#### Post-Imputation
The post imputation polyserial correlation was also computed using
the polychoric function, with no setting
smooth = TRUE and correct = 0.01.
The minimum correlation was -0.466. The maximum correlation was 0.851.
From the EFAtools documentation:
Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.
Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not
PCA) - fm = “wls” (weighted least squares because pa gave errors and
weighted recommended for ordinal data. - use = “all.obs” (since we have
imputed missing values, we can use all data points) - cor = “poly” (use
polychoric correlation matrix) - n.iter = 100 (run for 100
iterations)
The suggested number of factors is 13.
MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.
| Number of Factors | MAP value |
|---|---|
| 1 | 0.0271 |
| 2 | 0.0232 |
| 3 | 0.0182 |
| 4 | 0.0160 |
| 5 | 0.0146 |
| 6 | 0.0142 |
| 7 | 0.0141 |
| 8 | 0.0132 |
| 9 | 0.0130 |
| 10 | 0.0127 |
| 11 | 0.0123 |
| 12 | 0.0127 |
| 13 | 0.0127 |
| 14 | 0.0127 |
| 15 | 0.0132 |
| 16 | 0.0138 |
| 17 | 0.0145 |
| 18 | 0.0149 |
## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1321 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.
Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.7162758. Should be > 0.9; need reference)
| fanal17.communality | |
|---|---|
| TRAIN01 | 0.53 |
| TRAIN02 | 0.47 |
| TRAIN03 | 0.58 |
| TRAIN04 | 0.59 |
| TRAIN07 | 0.61 |
| AGG09 | 0.83 |
| AGG10 | 0.70 |
| AGG14 | 0.52 |
| AGG15 | 0.81 |
| AGG16 | 0.76 |
| AGG18 | 0.74 |
| AGG19 | 0.77 |
| AGG20 | 0.58 |
| FEAR21 | 0.85 |
| FEAR22 | 0.47 |
| FEAR23 | 0.81 |
| FEAR24 | 0.87 |
| FEAR25 | 0.61 |
| FEAR26 | 0.45 |
| FEAR27 | 0.89 |
| FEAR28 | 0.67 |
| FEAR29 | 0.53 |
| FEAR30 | 0.65 |
| FEAR31 | 0.66 |
| SEPR32 | 0.67 |
| SEPR33 | 0.66 |
| SEPR34 | 0.71 |
| EXCITE35 | 0.48 |
| EXCITE36 | 0.57 |
| EXCITE37 | 0.66 |
| EXCITE38 | 0.68 |
| ATT39 | 0.63 |
| ATT40 | 0.49 |
| ATT41 | 0.32 |
| PLAY43 | 0.57 |
| PLAY44 | 0.82 |
| PLAY45 | 0.76 |
| PLAY46 | 0.74 |
| IMP47 | 0.60 |
| IMP48 | 0.61 |
| MISC51 | 0.54 |
| MISC52 | 0.61 |
| MISC53 | 0.54 |
| MISC54 | 0.62 |
| MISC55 | 0.76 |
| MISC56 | 0.64 |
| MISC59 | 0.58 |
| MISC60 | 0.58 |
| MISC61 | 0.70 |
| MISC62 | 0.57 |
| MISC63 | 0.53 |
| MISC64 | 0.64 |
| MISC65 | 0.64 |
| MISC66 | 0.69 |
| MISC67 | 0.62 |
| MISC69 | 0.23 |
There are 2 items with communality < 0.40.
| fanal17.communality | item | |
|---|---|---|
| ATT41 | 0.32 | ATT41 |
| MISC69 | 0.23 | MISC69 |
| PA16 | PA1 | PA3 | PA2 | PA7 | PA5 | PA6 | PA4 | PA9 | PA8 | PA11 | PA15 | PA14 | PA10 | PA12 | PA17 | PA13 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| TRAIN01 | -0.02 | 0.15 | -0.04 | -0.02 | -0.09 | 0.00 | -0.06 | 0.01 | -0.03 | 0.44 | 0.08 | -0.01 | -0.02 | 0.08 | -0.07 | 0.06 | 0.35 |
| TRAIN02 | -0.03 | 0.05 | 0.07 | 0.00 | 0.05 | 0.01 | 0.03 | -0.08 | 0.06 | 0.65 | 0.03 | 0.03 | 0.02 | 0.03 | -0.02 | -0.06 | -0.15 |
| TRAIN03 | -0.03 | -0.05 | -0.03 | -0.05 | 0.03 | 0.05 | 0.02 | 0.03 | -0.07 | 0.72 | 0.05 | 0.04 | 0.05 | 0.01 | 0.05 | 0.01 | 0.02 |
| TRAIN04 | 0.07 | 0.32 | -0.04 | -0.02 | -0.02 | 0.02 | 0.04 | -0.05 | 0.02 | 0.47 | -0.04 | 0.16 | -0.07 | -0.04 | -0.15 | 0.00 | 0.13 |
| TRAIN07 | 0.07 | 0.61 | -0.10 | -0.05 | -0.06 | 0.03 | -0.02 | 0.02 | 0.01 | 0.23 | -0.01 | 0.01 | -0.05 | -0.02 | 0.01 | 0.07 | 0.03 |
| AGG09 | 0.21 | -0.02 | 0.73 | 0.02 | 0.06 | -0.06 | -0.04 | -0.03 | -0.04 | 0.01 | 0.07 | 0.06 | 0.01 | -0.13 | 0.11 | 0.10 | 0.17 |
| AGG10 | -0.05 | -0.01 | 0.82 | 0.07 | -0.03 | 0.13 | 0.00 | 0.06 | 0.02 | 0.01 | 0.01 | 0.02 | -0.05 | 0.03 | 0.02 | -0.03 | -0.09 |
| AGG14 | 0.05 | 0.08 | 0.64 | 0.08 | -0.01 | 0.15 | 0.04 | 0.07 | 0.00 | -0.03 | -0.10 | -0.02 | -0.14 | 0.15 | 0.04 | 0.07 | -0.02 |
| AGG15 | 0.28 | 0.04 | 0.74 | -0.07 | 0.05 | -0.05 | 0.00 | 0.12 | -0.07 | 0.00 | 0.07 | -0.01 | 0.10 | 0.04 | -0.11 | -0.08 | 0.00 |
| AGG16 | -0.15 | -0.01 | 0.29 | -0.06 | 0.05 | -0.05 | -0.04 | 0.47 | 0.33 | 0.11 | -0.05 | 0.01 | -0.02 | -0.17 | 0.14 | 0.11 | 0.04 |
| AGG18 | -0.16 | -0.08 | 0.27 | -0.03 | -0.01 | -0.03 | -0.11 | 0.51 | 0.28 | 0.07 | -0.02 | 0.06 | 0.07 | -0.11 | 0.15 | 0.12 | 0.07 |
| AGG19 | 0.04 | 0.04 | 0.04 | 0.06 | 0.01 | 0.00 | 0.10 | 0.82 | 0.02 | -0.01 | 0.08 | -0.09 | 0.06 | -0.04 | -0.06 | 0.02 | 0.06 |
| AGG20 | 0.02 | 0.03 | -0.06 | -0.02 | 0.02 | 0.01 | 0.00 | 0.74 | -0.06 | -0.05 | 0.06 | 0.17 | -0.11 | 0.11 | -0.02 | -0.07 | -0.07 |
| FEAR21 | 0.82 | 0.01 | 0.09 | 0.00 | 0.03 | -0.01 | 0.00 | 0.02 | 0.09 | -0.02 | 0.08 | 0.02 | 0.01 | -0.03 | 0.05 | -0.02 | 0.04 |
| FEAR22 | 0.30 | 0.07 | -0.20 | -0.04 | 0.14 | 0.07 | 0.00 | 0.20 | -0.10 | 0.08 | 0.02 | -0.05 | -0.07 | 0.11 | 0.02 | 0.30 | -0.24 |
| FEAR23 | 0.74 | -0.03 | 0.17 | -0.04 | 0.03 | 0.07 | -0.02 | -0.02 | 0.15 | -0.01 | -0.03 | 0.00 | 0.04 | -0.05 | 0.00 | 0.10 | -0.02 |
| FEAR24 | 0.79 | 0.03 | 0.13 | -0.10 | -0.02 | -0.03 | 0.04 | -0.01 | 0.17 | -0.01 | 0.04 | -0.01 | 0.02 | -0.03 | 0.07 | -0.03 | -0.03 |
| FEAR25 | 0.36 | 0.05 | -0.10 | 0.06 | 0.20 | 0.08 | -0.02 | 0.08 | -0.03 | 0.08 | -0.01 | 0.03 | -0.13 | 0.08 | 0.02 | 0.45 | -0.04 |
| FEAR26 | 0.34 | 0.02 | 0.03 | 0.05 | -0.02 | 0.04 | -0.02 | 0.09 | 0.09 | 0.05 | 0.42 | 0.02 | 0.02 | 0.04 | 0.02 | -0.08 | -0.08 |
| FEAR27 | 0.16 | 0.02 | -0.04 | 0.02 | 0.04 | 0.03 | 0.01 | 0.04 | 0.88 | -0.02 | 0.01 | 0.01 | -0.03 | 0.04 | -0.02 | -0.01 | 0.00 |
| FEAR28 | 0.43 | 0.06 | -0.06 | 0.03 | 0.30 | 0.05 | 0.04 | 0.00 | 0.03 | 0.04 | 0.18 | 0.05 | -0.06 | -0.10 | 0.00 | 0.18 | -0.14 |
| FEAR29 | -0.02 | -0.02 | 0.02 | 0.02 | -0.02 | 0.03 | 0.01 | 0.00 | 0.03 | 0.06 | 0.72 | -0.05 | 0.00 | 0.04 | 0.04 | -0.04 | 0.04 |
| FEAR30 | -0.03 | -0.01 | -0.01 | 0.02 | 0.06 | 0.09 | -0.01 | 0.07 | 0.00 | 0.00 | 0.74 | 0.02 | -0.04 | 0.04 | -0.04 | 0.05 | -0.03 |
| FEAR31 | 0.11 | 0.02 | -0.12 | 0.00 | 0.06 | 0.03 | 0.01 | -0.02 | 0.73 | 0.01 | 0.10 | 0.04 | -0.06 | 0.05 | 0.01 | 0.02 | -0.03 |
| SEPR32 | 0.04 | 0.00 | 0.04 | -0.08 | -0.06 | 0.75 | 0.08 | 0.03 | 0.01 | -0.03 | 0.07 | 0.05 | 0.02 | -0.12 | 0.07 | -0.02 | -0.06 |
| SEPR33 | -0.08 | 0.04 | 0.03 | 0.00 | 0.01 | 0.78 | 0.00 | -0.03 | 0.05 | 0.07 | 0.04 | 0.00 | 0.03 | 0.01 | 0.02 | -0.01 | -0.07 |
| SEPR34 | -0.01 | 0.00 | 0.04 | 0.01 | 0.06 | 0.80 | -0.02 | -0.04 | 0.01 | 0.01 | 0.02 | -0.01 | 0.02 | 0.04 | -0.03 | 0.01 | 0.16 |
| EXCITE35 | 0.12 | 0.04 | -0.03 | -0.08 | -0.07 | 0.12 | 0.56 | 0.04 | 0.02 | 0.08 | -0.06 | -0.04 | 0.14 | 0.04 | 0.13 | -0.05 | -0.02 |
| EXCITE36 | 0.01 | 0.00 | 0.00 | 0.14 | 0.02 | -0.05 | 0.63 | 0.00 | -0.08 | 0.01 | 0.06 | 0.04 | 0.13 | -0.05 | 0.06 | 0.01 | -0.05 |
| EXCITE37 | -0.02 | 0.04 | 0.03 | -0.04 | 0.01 | 0.01 | 0.83 | 0.02 | 0.04 | -0.01 | -0.02 | 0.01 | -0.02 | -0.01 | 0.01 | -0.08 | 0.05 |
| EXCITE38 | -0.02 | -0.13 | -0.01 | 0.05 | 0.03 | 0.00 | 0.78 | 0.02 | 0.00 | 0.01 | 0.01 | 0.06 | -0.06 | 0.02 | -0.03 | 0.12 | -0.01 |
| ATT39 | 0.05 | 0.03 | -0.01 | 0.06 | -0.03 | 0.01 | 0.07 | -0.03 | -0.02 | 0.00 | -0.02 | -0.09 | 0.09 | 0.08 | 0.75 | -0.09 | -0.06 |
| ATT40 | 0.02 | 0.15 | -0.03 | -0.13 | 0.05 | 0.07 | 0.04 | -0.08 | -0.04 | -0.08 | 0.12 | 0.17 | -0.17 | -0.08 | 0.50 | 0.10 | 0.15 |
| ATT41 | 0.02 | -0.01 | -0.13 | 0.05 | -0.02 | 0.09 | -0.01 | 0.06 | -0.04 | 0.02 | -0.02 | 0.12 | 0.06 | 0.20 | 0.40 | 0.14 | 0.03 |
| PLAY43 | -0.29 | -0.01 | -0.22 | 0.49 | 0.00 | -0.03 | 0.08 | -0.08 | 0.09 | -0.05 | -0.02 | 0.01 | 0.10 | 0.05 | -0.07 | 0.09 | -0.05 |
| PLAY44 | -0.02 | 0.05 | -0.02 | 0.86 | -0.02 | -0.03 | 0.06 | 0.08 | 0.01 | -0.02 | 0.06 | 0.06 | 0.03 | -0.11 | 0.03 | -0.02 | 0.02 |
| PLAY45 | -0.01 | -0.01 | 0.06 | 0.81 | -0.05 | -0.06 | -0.02 | -0.07 | 0.06 | -0.05 | 0.00 | 0.03 | 0.10 | 0.00 | 0.05 | 0.02 | -0.07 |
| PLAY46 | 0.03 | -0.09 | 0.10 | 0.82 | 0.02 | 0.05 | 0.02 | 0.02 | -0.07 | 0.02 | -0.05 | -0.01 | -0.02 | 0.01 | -0.04 | -0.02 | 0.05 |
| IMP47 | 0.05 | -0.05 | 0.00 | 0.16 | 0.00 | -0.02 | 0.08 | 0.00 | 0.05 | 0.14 | -0.02 | 0.61 | 0.04 | 0.09 | -0.01 | -0.02 | 0.14 |
| IMP48 | -0.08 | 0.00 | 0.07 | 0.02 | -0.01 | 0.04 | 0.09 | 0.01 | 0.04 | 0.06 | 0.02 | 0.71 | 0.01 | 0.05 | -0.03 | 0.02 | -0.09 |
| MISC51 | 0.05 | 0.08 | -0.05 | -0.04 | 0.01 | 0.23 | 0.05 | 0.12 | -0.07 | 0.03 | -0.04 | 0.07 | 0.04 | 0.19 | -0.08 | 0.03 | 0.52 |
| MISC52 | -0.05 | 0.02 | 0.13 | -0.09 | 0.01 | -0.06 | 0.01 | -0.04 | 0.09 | 0.02 | 0.06 | 0.04 | 0.01 | 0.72 | 0.09 | 0.07 | -0.05 |
| MISC53 | -0.04 | -0.02 | -0.02 | -0.08 | 0.01 | 0.01 | 0.01 | 0.04 | 0.03 | 0.04 | 0.08 | 0.11 | 0.01 | 0.61 | 0.01 | -0.06 | 0.20 |
| MISC54 | -0.01 | 0.13 | -0.01 | -0.03 | 0.65 | -0.03 | 0.05 | -0.02 | 0.01 | 0.02 | 0.11 | 0.01 | -0.10 | 0.05 | 0.05 | 0.06 | -0.02 |
| MISC55 | -0.01 | -0.04 | 0.00 | 0.04 | 0.88 | 0.05 | 0.00 | 0.04 | 0.01 | 0.03 | -0.03 | -0.08 | 0.01 | -0.02 | -0.01 | 0.01 | -0.01 |
| MISC56 | -0.07 | 0.04 | 0.05 | -0.09 | 0.80 | -0.06 | -0.01 | -0.04 | 0.05 | -0.03 | 0.03 | 0.08 | 0.08 | 0.00 | -0.03 | -0.08 | 0.04 |
| MISC59 | 0.07 | 0.10 | -0.10 | 0.05 | 0.01 | 0.26 | -0.04 | 0.10 | -0.08 | -0.05 | 0.03 | 0.44 | 0.32 | 0.01 | -0.01 | -0.01 | 0.04 |
| MISC60 | 0.01 | -0.03 | -0.07 | 0.07 | 0.06 | 0.02 | 0.05 | -0.09 | -0.01 | 0.06 | 0.01 | 0.06 | 0.67 | 0.03 | 0.07 | 0.05 | 0.01 |
| MISC61 | 0.08 | -0.01 | -0.01 | 0.18 | -0.01 | 0.12 | 0.08 | 0.07 | -0.11 | -0.01 | -0.08 | 0.03 | 0.66 | -0.02 | 0.03 | -0.01 | -0.01 |
| MISC62 | -0.16 | 0.26 | 0.08 | -0.12 | -0.07 | -0.03 | 0.03 | 0.09 | 0.29 | 0.01 | 0.07 | 0.02 | 0.25 | -0.04 | 0.00 | 0.35 | 0.07 |
| MISC63 | -0.09 | 0.21 | 0.11 | -0.09 | -0.02 | -0.06 | 0.16 | -0.10 | 0.05 | -0.04 | 0.12 | 0.06 | 0.18 | 0.07 | -0.08 | 0.50 | 0.09 |
| MISC64 | -0.09 | 0.82 | 0.05 | 0.03 | 0.04 | 0.03 | -0.02 | 0.01 | 0.01 | -0.01 | 0.00 | -0.07 | 0.02 | 0.03 | 0.03 | -0.05 | 0.02 |
| MISC65 | -0.08 | 0.70 | 0.02 | -0.02 | 0.00 | 0.02 | -0.02 | 0.06 | 0.06 | 0.05 | 0.03 | 0.01 | 0.01 | 0.05 | 0.01 | 0.05 | 0.07 |
| MISC66 | 0.18 | 0.57 | 0.01 | -0.07 | 0.15 | 0.04 | -0.04 | -0.07 | -0.02 | 0.02 | 0.06 | 0.12 | -0.04 | -0.04 | 0.02 | 0.11 | -0.04 |
| MISC67 | 0.16 | 0.56 | 0.01 | -0.12 | 0.12 | 0.03 | -0.04 | 0.03 | -0.02 | -0.03 | 0.02 | 0.12 | 0.00 | -0.02 | 0.08 | 0.08 | -0.15 |
| MISC69 | 0.10 | 0.04 | -0.05 | 0.04 | 0.24 | 0.12 | 0.02 | 0.04 | 0.09 | -0.01 | -0.18 | 0.04 | -0.03 | 0.08 | 0.08 | 0.09 | 0.24 |
| largest | maximum | itemNames | itemDescriptions | |
|---|---|---|---|---|
| 40 | PA1 | 0.82 | MISC64 | When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects |
| 41 | PA1 | 0.70 | MISC65 | Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.) |
| 42 | PA1 | 0.57 | MISC66 | Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work |
| 43 | PA1 | 0.56 | MISC67 | Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work |
| 56 | PA1 | 0.61 | TRAIN07 | Unfocused; is easily distracted by interesting sights, sounds or smells |
| 30 | PA10 | 0.72 | MISC52 | Begs persistently for food when people are eating |
| 31 | PA10 | 0.61 | MISC53 | Steals food |
| 21 | PA11 | 0.42 | FEAR26 | When examined/treated by a veterinarian |
| 24 | PA11 | 0.72 | FEAR29 | When having nails trimmed, or feet touched/handled |
| 25 | PA11 | 0.74 | FEAR30 | When groomed or bathed |
| 9 | PA12 | 0.75 | ATT39 | Displays a strong attachment for you or another familiar person |
| 10 | PA12 | 0.50 | ATT40 | Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler |
| 11 | PA12 | 0.40 | ATT41 | Tends to nudge or paw you (or others) for attention |
| 29 | PA13 | 0.52 | MISC51 | Escapes or would escape from home, yard or kennel given the chance |
| 44 | PA13 | 0.24 | MISC69 | Chases/follows shadows, light spots, etc. |
| 36 | PA14 | 0.67 | MISC60 | Playful, puppyish, boisterous |
| 37 | PA14 | 0.66 | MISC61 | Active, energetic, always on the go |
| 27 | PA15 | 0.61 | IMP47 | Impulsive; doesn’t seem to think before s/he acts |
| 28 | PA15 | 0.71 | IMP48 | Becomes frustrated/impatient in a wide range of situations |
| 35 | PA15 | 0.44 | MISC59 | Hyperactive, restless, has trouble settling down |
| 16 | PA16 | 0.82 | FEAR21 | When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel |
| 17 | PA16 | 0.30 | FEAR22 | In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.) |
| 18 | PA16 | 0.74 | FEAR23 | When an unfamiliar person visits your home or approaches the dog when in his/her home kennel |
| 19 | PA16 | 0.79 | FEAR24 | When an unfamiliar person tries to touch or pet the dog |
| 23 | PA16 | 0.43 | FEAR28 | When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.) |
| 20 | PA17 | 0.45 | FEAR25 | In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc. |
| 38 | PA17 | 0.35 | MISC62 | Becomes highly excited and/or distracted when encountering unfamiliar dogs |
| 39 | PA17 | 0.50 | MISC63 | Becomes highly excited and/or distracted when encountering unfamiliar people |
| 45 | PA2 | 0.49 | PLAY43 | Eagerly engages in play with new/unfamiliar people |
| 46 | PA2 | 0.86 | PLAY44 | Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person |
| 47 | PA2 | 0.81 | PLAY45 | Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown |
| 48 | PA2 | 0.82 | PLAY46 | Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task |
| 1 | PA3 | 0.73 | AGG09 | Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash |
| 2 | PA3 | 0.82 | AGG10 | Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel |
| 3 | PA3 | 0.64 | AGG14 | When strangers walk past when the dog is in his/her home run or kennel |
| 4 | PA3 | 0.74 | AGG15 | When an unfamiliar person tries to touch or pet the dog |
| 5 | PA4 | 0.47 | AGG16 | When approached directly by an unfamiliar dog while being walked/exercised on a leash |
| 6 | PA4 | 0.51 | AGG18 | When barked, growled, or lunged at by another dog |
| 7 | PA4 | 0.82 | AGG19 | Towards other familiar dogs |
| 8 | PA4 | 0.74 | AGG20 | When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog |
| 49 | PA5 | 0.75 | SEPR32 | Restlessness/agitation/pacing when left alone |
| 50 | PA5 | 0.78 | SEPR33 | Barking or whining when left alone |
| 51 | PA5 | 0.80 | SEPR34 | Chewing/scratching at doors, floor, fencing, etc., when left alone |
| 12 | PA6 | 0.56 | EXCITE35 | Excitable when you first arrive home, or at the dog’s kennel, after a brief absence |
| 13 | PA6 | 0.63 | EXCITE36 | Excitable when playing with you or other familiar persons |
| 14 | PA6 | 0.83 | EXCITE37 | Excitable just before being taken out for a walk |
| 15 | PA6 | 0.78 | EXCITE38 | Excitable just before being taken out for work or training |
| 32 | PA7 | 0.65 | MISC54 | Reluctant to/nervous about crossing grates or other unfamiliar surfaces |
| 33 | PA7 | 0.88 | MISC55 | Reluctant to/nervous about crossing shiny or slippery floors |
| 34 | PA7 | 0.80 | MISC56 | Nervous or frightened when ascending or descending some types of stairs |
| 52 | PA8 | 0.44 | TRAIN01 | Is hard to recall when off the leash |
| 53 | PA8 | 0.65 | TRAIN02 | Is slow to obey a ‘sit’ command |
| 54 | PA8 | 0.72 | TRAIN03 | Is slow to obey a ‘stay’ command |
| 55 | PA8 | 0.47 | TRAIN04 | Has difficulty attending/listening to things you say or do |
| 22 | PA9 | 0.88 | FEAR27 | When approached directly by an unfamiliar dog |
| 26 | PA9 | 0.73 | FEAR31 | When barked, growled, or lunged at by an unfamiliar dog |
| PA16 | PA1 | PA3 | PA2 | PA7 | PA5 | PA6 | PA4 | PA9 | PA8 | PA11 | PA15 | PA14 | PA10 | PA12 | PA17 | PA13 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| alpha | 0.761 | 0.805 | 0.76 | 0.812 | 0.718 | 0.735 | 0.787 | 0.752 | 0.802 | 0.693 | 0.613 | 0.683 | 0.71 | 0.622 | 0.494 | 0.558 | 0.159 |
omega is thought to be better measure of reliability than alpha, because it looks at the relationships between all the items rather than just the ones within each factor. It’s different than alpha because it assumes that there is a genral factor, g, that all items have in common. This is listed as the first row of the table below.
There are three omegas for each factor:
From EFAtools::OMEGA documentation:
Omegas refer to the correlation between a factor and a unit-weighted composite score and thus the true score variance in a unit-weighted composite based on the respective indicators. Omega total is the total true score variance in a composite. Omega hierarchical is the true score variance in a composite that is attributable to the general factor, and omega subscale is the true score variance in a composite attributable to all subscales / group factors (for the whole scale) or to the specific subscale / group factor (for subscale composites).
Interpretation of omega_subscale
no universal guideline
0.50 is minimum, 0.75 preferable (watkins books,rodrigues16, zimbarg2005
## Omega total, omega hierarchical, omega subscale, H index, explained common variance (ECV), and percent of uncontaminated correlations (PUC) for the general factor (top row) and omegas and H index for the group factors:
##
## tot hier sub H ECV PUC
## g 0.950 0.600 0.162 0.893 0.242 0.953
## F1 0.832 0.400 0.432 0.683
## F2 0.631 0.076 0.555 0.612
## F3 0.705 0.253 0.452 0.596
## F4 0.633 0.090 0.543 0.627
## F5 0.365 0.128 0.237 0.293
## F6 0.556 0.002 0.555 0.619
## F7 0.588 0.162 0.426 0.571
## F8 0.792 0.289 0.503 0.785
## F9 0.631 0.371 0.260 0.358
## F10 0.797 0.063 0.734 0.856
## F11 0.812 0.110 0.702 0.815
## F12 0.689 0.156 0.534 0.750
## F13 0.841 0.156 0.685 0.767
## F14 0.760 0.025 0.736 0.820
## F15 0.851 0.207 0.644 0.763
## F16 0.661 0.184 0.477 0.642
## F17 0.826 0.213 0.613 0.730
include reference on why imputation is better than removing observations, pairwise removing is biased, using means isn’t good.
Categorical missing values using multiple Correspondence Analysis (also called Missing Fuzzy Average method) Josseet al (201 0)
This function tests whether a correlation matrix is significantly different from an identity matrix (Bartlett, 1951). If the Bartlett’s test is not significant, the correlation matrix is not suitable for factor analysis because the variables show too little covariance.
## Warning in polychoric(ddNum18, smooth = TRUE, correct = 0.01): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1318 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.
The chi-squared for the Bartlett test is 4.0386817^{4} with 1540 DF, p = 0e+00.
From EFAtools::KMO documentation:
The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis
The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.
## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.
[1] 0.8554013
## Warning in polychoric(imputedNumericDF18, smooth = TRUE, correct = 0.01): The
## items do not have an equal number of response alternatives, global set to
## FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1317 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
This is a test that the matrix is an identity matrix. This would mean that the correlations were not significantly different from 0. If it’s not significant, the matrix is not suitable because the variables show too little covariance.
The chi-squared for the Bartlett test is 3.8935509^{4} with 1540 DF, p = 0e+00.
From EFAtools::KMO documentation:
The KMO represents the degree to which each observed variable is predicted by the other variables in the dataset and with this indicates the suitability for factor analysis
The numeric version of the dataset is used because stats::cor is used to find the correlation and it requires numeric input. Used option for Spearman correlation because of ordered variables.
## ℹ 'x' was not a correlation matrix. Correlations are found from entered raw data.
[1] 0.8554013
For factor analysis, it is recommended that some of the item
correlationsshould be between 0.3 and 0.9. Polychoric correlations were
computed using the polychoric function in the
psych package in R with options smooth = TRUE
to adjust for non-positive-definite matrices and
correct = 0.01 to avoid computation problems with
covariance of zero.
The minimum correlation in this data set is -0.477. The maximum correlation in this data set is 0.856.
#### Post-Imputation
The post imputation polyserial correlation was also computed using
the polychoric function, with no setting
smooth = TRUE and correct = 0.01.
The minimum correlation was -0.466. The maximum correlation was 0.851.
From the EFAtools documentation:
Various methods for performing parallel analysis. This function uses future_lapply for which a parallel processing plan can be selected. To do so, call library(future) and, for example, plan(multisession); see examples.
Settings Used:
- n.obs = 1117 - eigen_type = “EFA” - fa = “fa” (factor analysis not
PCA) - fm = “wls” (weighted least squares because pa gave errors and
weighted recommended for ordinal data. - use = “all.obs” (since we have
imputed missing values, we can use all data points) - cor = “poly” (use
polychoric correlation matrix) - n.iter = 100 (run for 100
iterations)
The suggested number of factors is 13.
MAP is recommended as a way to find the number of factors when the items are ordinal. The lowest value indicates the best number of factors.
| Number of Factors | MAP value |
|---|---|
| 1 | 0.0269 |
| 2 | 0.0229 |
| 3 | 0.0180 |
| 4 | 0.0158 |
| 5 | 0.0148 |
| 6 | 0.0144 |
| 7 | 0.0141 |
| 8 | 0.0130 |
| 9 | 0.0127 |
| 10 | 0.0122 |
| 11 | 0.0121 |
| 12 | 0.0124 |
| 13 | 0.0125 |
| 14 | 0.0125 |
| 15 | 0.0129 |
| 16 | 0.0135 |
| 17 | 0.0140 |
| 18 | 0.0148 |
## Warning in polychoric(r, correct = correct, weight = weight): The items do not
## have an equal number of response alternatives, global set to FALSE.
## Warning in matpLower(x, nvar, gminx, gmaxx, gminy, gmaxy): 1317 cells were
## adjusted for 0 values using the correction for continuity. Examine your data
## carefully.
Although the chi-square test of goodness of fit is sensitive to departures from normality like the C-BARQ items, Hopper et al (2008) recommend always reporting it.
Tucker-Lewis Index of Factoring Reliability/Non-Norm Fit Index: 0.733559. Should be > 0.9; need reference)
| fanal18.communality | |
|---|---|
| TRAIN01 | 0.44 |
| TRAIN02 | 0.43 |
| TRAIN03 | 0.60 |
| TRAIN04 | 0.59 |
| TRAIN07 | 0.62 |
| AGG09 | 0.80 |
| AGG10 | 0.73 |
| AGG14 | 0.58 |
| AGG15 | 0.80 |
| AGG16 | 0.76 |
| AGG18 | 0.74 |
| AGG19 | 0.77 |
| AGG20 | 0.58 |
| FEAR21 | 0.84 |
| FEAR22 | 0.50 |
| FEAR23 | 0.81 |
| FEAR24 | 0.92 |
| FEAR25 | 0.62 |
| FEAR26 | 0.44 |
| FEAR27 | 0.86 |
| FEAR28 | 0.67 |
| FEAR29 | 0.67 |
| FEAR30 | 0.61 |
| FEAR31 | 0.73 |
| SEPR32 | 0.71 |
| SEPR33 | 0.65 |
| SEPR34 | 0.66 |
| EXCITE35 | 0.48 |
| EXCITE36 | 0.57 |
| EXCITE37 | 0.66 |
| EXCITE38 | 0.69 |
| ATT39 | 0.61 |
| ATT40 | 0.48 |
| ATT41 | 0.32 |
| PLAY43 | 0.57 |
| PLAY44 | 0.83 |
| PLAY45 | 0.78 |
| PLAY46 | 0.73 |
| IMP47 | 0.59 |
| IMP48 | 0.60 |
| IMP49 | 0.38 |
| MISC52 | 0.60 |
| MISC53 | 0.64 |
| MISC54 | 0.62 |
| MISC55 | 0.75 |
| MISC56 | 0.67 |
| MISC59 | 0.58 |
| MISC60 | 0.61 |
| MISC61 | 0.73 |
| MISC62 | 0.62 |
| MISC63 | 0.57 |
| MISC64 | 0.64 |
| MISC65 | 0.64 |
| MISC66 | 0.70 |
| MISC67 | 0.67 |
| MISC69 | 0.53 |
There are 2 items with communality < 0.40.
| fanal18.communality | item | |
|---|---|---|
| ATT41 | 0.32 | ATT41 |
| IMP49 | 0.38 | IMP49 |
| PA18 | PA1 | PA2 | PA3 | PA7 | PA5 | PA6 | PA4 | PA9 | PA8 | PA15 | PA13 | PA11 | PA17 | PA10 | PA14 | PA12 | PA16 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| TRAIN01 | -0.07 | 0.16 | -0.07 | 0.00 | -0.11 | 0.01 | -0.07 | 0.00 | -0.04 | 0.46 | 0.06 | -0.02 | 0.08 | 0.10 | 0.07 | -0.10 | -0.03 | 0.08 |
| TRAIN02 | -0.01 | 0.05 | 0.02 | 0.05 | 0.07 | 0.01 | 0.03 | -0.07 | 0.08 | 0.62 | 0.01 | 0.01 | 0.02 | -0.07 | 0.03 | -0.01 | 0.03 | -0.10 |
| TRAIN03 | -0.02 | -0.05 | -0.03 | -0.06 | 0.04 | 0.07 | 0.01 | 0.05 | -0.08 | 0.74 | 0.02 | 0.03 | 0.02 | 0.00 | 0.05 | 0.05 | 0.02 | -0.02 |
| TRAIN04 | 0.05 | 0.32 | -0.05 | -0.03 | -0.04 | 0.02 | 0.04 | -0.06 | 0.02 | 0.47 | 0.16 | -0.04 | -0.01 | 0.01 | -0.04 | -0.17 | -0.01 | 0.12 |
| TRAIN07 | 0.04 | 0.59 | -0.07 | -0.07 | -0.08 | 0.02 | -0.02 | 0.01 | 0.01 | 0.23 | 0.00 | -0.03 | 0.02 | 0.05 | -0.03 | 0.01 | 0.07 | 0.10 |
| AGG09 | 0.30 | -0.04 | 0.02 | 0.61 | 0.07 | -0.05 | -0.06 | 0.01 | -0.10 | 0.04 | 0.08 | -0.01 | 0.06 | 0.19 | -0.11 | 0.10 | -0.12 | 0.05 |
| AGG10 | -0.06 | -0.01 | 0.04 | 0.83 | -0.02 | 0.09 | 0.00 | 0.05 | 0.05 | 0.01 | 0.02 | 0.00 | 0.03 | -0.03 | -0.02 | 0.02 | -0.02 | -0.07 |
| AGG14 | -0.02 | 0.09 | 0.01 | 0.73 | -0.06 | 0.07 | 0.06 | 0.02 | 0.04 | -0.06 | -0.02 | -0.04 | -0.01 | -0.03 | 0.06 | 0.02 | 0.12 | 0.14 |
| AGG15 | 0.39 | 0.03 | -0.05 | 0.60 | 0.08 | -0.04 | -0.01 | 0.15 | -0.11 | 0.00 | -0.02 | 0.06 | 0.04 | 0.03 | 0.06 | -0.11 | -0.15 | -0.07 |
| AGG16 | -0.07 | -0.04 | -0.03 | 0.21 | 0.06 | -0.03 | -0.05 | 0.53 | 0.25 | 0.11 | 0.01 | -0.07 | -0.06 | 0.18 | -0.13 | 0.14 | -0.09 | 0.04 |
| AGG18 | -0.09 | -0.09 | 0.00 | 0.20 | 0.00 | -0.01 | -0.12 | 0.56 | 0.22 | 0.08 | 0.06 | 0.02 | -0.04 | 0.19 | -0.08 | 0.14 | -0.07 | 0.03 |
| AGG19 | 0.07 | 0.03 | 0.08 | 0.00 | 0.02 | 0.03 | 0.09 | 0.84 | -0.02 | 0.01 | -0.08 | 0.01 | 0.05 | 0.05 | 0.00 | -0.07 | 0.00 | 0.00 |
| AGG20 | -0.05 | 0.04 | -0.06 | 0.00 | 0.00 | -0.01 | 0.01 | 0.71 | -0.02 | -0.07 | 0.17 | -0.05 | 0.09 | -0.17 | 0.08 | -0.03 | 0.14 | 0.01 |
| FEAR21 | 0.82 | 0.02 | -0.01 | 0.06 | 0.02 | -0.01 | 0.00 | 0.00 | 0.08 | -0.01 | 0.03 | 0.03 | 0.08 | -0.06 | -0.03 | 0.03 | 0.07 | 0.05 |
| FEAR22 | 0.14 | 0.06 | -0.09 | -0.07 | 0.11 | 0.02 | 0.01 | 0.15 | 0.00 | 0.06 | -0.05 | 0.02 | 0.03 | 0.00 | 0.02 | 0.02 | 0.55 | -0.04 |
| FEAR23 | 0.76 | -0.04 | -0.02 | 0.12 | 0.02 | 0.07 | -0.03 | -0.03 | 0.12 | 0.00 | 0.01 | 0.02 | -0.04 | 0.06 | -0.05 | -0.01 | 0.11 | 0.03 |
| FEAR24 | 0.90 | 0.01 | -0.03 | 0.00 | 0.00 | 0.00 | 0.03 | 0.00 | 0.10 | -0.01 | -0.03 | -0.04 | 0.00 | 0.01 | 0.03 | 0.06 | -0.02 | -0.02 |
| FEAR25 | 0.23 | 0.02 | 0.01 | -0.01 | 0.13 | 0.04 | -0.02 | 0.03 | 0.00 | 0.06 | 0.06 | -0.07 | 0.04 | 0.20 | -0.01 | 0.01 | 0.49 | 0.17 |
| FEAR26 | 0.39 | 0.02 | 0.08 | -0.03 | 0.01 | 0.06 | -0.02 | 0.09 | 0.08 | 0.03 | 0.03 | -0.01 | 0.36 | -0.05 | 0.06 | 0.02 | -0.01 | -0.09 |
| FEAR27 | 0.16 | 0.01 | 0.01 | 0.00 | 0.02 | 0.01 | 0.01 | 0.05 | 0.84 | -0.03 | 0.00 | -0.02 | 0.02 | 0.03 | 0.02 | -0.03 | -0.04 | 0.06 |
| FEAR28 | 0.39 | 0.04 | 0.04 | -0.05 | 0.30 | 0.06 | 0.04 | -0.02 | 0.06 | 0.04 | 0.05 | -0.05 | 0.13 | 0.06 | -0.12 | 0.01 | 0.27 | -0.07 |
| FEAR29 | -0.06 | -0.01 | -0.05 | 0.06 | -0.04 | -0.02 | 0.00 | -0.03 | 0.05 | 0.03 | -0.03 | 0.05 | 0.84 | -0.02 | -0.02 | 0.03 | -0.03 | 0.01 |
| FEAR30 | 0.03 | 0.00 | 0.04 | -0.05 | 0.09 | 0.11 | -0.02 | 0.10 | 0.00 | -0.02 | 0.01 | -0.07 | 0.66 | 0.07 | 0.06 | -0.04 | 0.02 | -0.03 |
| FEAR31 | 0.04 | 0.03 | -0.02 | -0.03 | 0.04 | 0.01 | 0.01 | -0.04 | 0.80 | 0.00 | 0.05 | -0.02 | 0.09 | -0.01 | 0.01 | 0.00 | 0.05 | -0.03 |
| SEPR32 | 0.07 | -0.02 | -0.03 | 0.00 | -0.03 | 0.82 | 0.07 | 0.04 | -0.01 | -0.03 | 0.02 | -0.02 | 0.01 | 0.02 | -0.07 | 0.06 | -0.02 | -0.07 |
| SEPR33 | -0.08 | 0.03 | 0.02 | 0.03 | 0.01 | 0.78 | -0.01 | -0.03 | 0.05 | 0.07 | -0.03 | 0.02 | 0.02 | -0.02 | 0.03 | 0.01 | 0.03 | -0.01 |
| SEPR34 | -0.03 | 0.00 | 0.00 | 0.06 | 0.03 | 0.77 | -0.04 | -0.04 | -0.01 | 0.03 | 0.01 | 0.03 | 0.02 | 0.01 | 0.05 | -0.06 | -0.02 | 0.12 |
| EXCITE35 | 0.13 | 0.04 | -0.06 | -0.03 | -0.06 | 0.13 | 0.55 | 0.04 | 0.02 | 0.08 | -0.07 | 0.15 | -0.07 | -0.02 | 0.06 | 0.13 | -0.02 | -0.01 |
| EXCITE36 | 0.01 | 0.00 | 0.15 | 0.00 | 0.03 | -0.04 | 0.62 | 0.00 | -0.06 | 0.02 | 0.04 | 0.13 | 0.04 | 0.03 | -0.04 | 0.07 | 0.01 | -0.07 |
| EXCITE37 | 0.01 | 0.05 | -0.03 | 0.01 | 0.01 | 0.03 | 0.82 | 0.03 | 0.03 | -0.01 | 0.02 | -0.02 | -0.02 | -0.01 | 0.01 | 0.01 | -0.11 | 0.00 |
| EXCITE38 | -0.06 | -0.13 | 0.03 | 0.03 | 0.01 | -0.02 | 0.78 | 0.00 | 0.02 | 0.00 | 0.07 | -0.02 | 0.03 | 0.06 | -0.01 | -0.03 | 0.11 | 0.05 |
| ATT39 | 0.05 | 0.03 | 0.06 | 0.02 | -0.03 | 0.00 | 0.07 | -0.02 | -0.01 | -0.01 | -0.09 | 0.10 | 0.00 | -0.10 | 0.06 | 0.74 | -0.01 | -0.01 |
| ATT40 | 0.05 | 0.13 | -0.10 | -0.05 | 0.05 | 0.11 | 0.03 | -0.06 | -0.08 | -0.06 | 0.19 | -0.20 | 0.09 | 0.14 | -0.04 | 0.49 | -0.02 | 0.06 |
| ATT41 | -0.03 | -0.01 | 0.03 | -0.07 | -0.05 | 0.08 | -0.02 | 0.04 | -0.03 | 0.01 | 0.09 | 0.10 | 0.02 | 0.05 | 0.16 | 0.40 | 0.16 | 0.13 |
| PLAY43 | -0.31 | -0.01 | 0.50 | -0.18 | 0.00 | -0.03 | 0.07 | -0.08 | 0.10 | -0.06 | -0.03 | 0.09 | -0.01 | 0.06 | 0.05 | -0.07 | 0.06 | 0.02 |
| PLAY44 | 0.01 | 0.05 | 0.88 | -0.05 | -0.01 | -0.01 | 0.04 | 0.09 | -0.02 | 0.00 | 0.05 | 0.00 | 0.03 | 0.00 | -0.08 | 0.02 | -0.04 | 0.01 |
| PLAY45 | 0.03 | -0.02 | 0.86 | 0.03 | -0.02 | -0.03 | -0.04 | -0.06 | 0.05 | -0.04 | 0.01 | 0.06 | -0.04 | 0.04 | 0.03 | 0.05 | 0.00 | -0.08 |
| PLAY46 | 0.00 | -0.08 | 0.79 | 0.12 | 0.00 | 0.04 | 0.02 | 0.00 | -0.07 | 0.03 | 0.01 | 0.01 | -0.04 | -0.08 | -0.01 | -0.05 | 0.02 | 0.06 |
| IMP47 | 0.02 | -0.05 | 0.13 | 0.01 | -0.02 | -0.02 | 0.08 | -0.01 | 0.05 | 0.13 | 0.61 | 0.09 | 0.02 | 0.00 | 0.09 | -0.02 | -0.04 | 0.11 |
| IMP48 | -0.08 | -0.02 | 0.04 | 0.05 | 0.01 | 0.06 | 0.10 | 0.02 | 0.06 | 0.04 | 0.67 | 0.03 | 0.00 | 0.03 | 0.06 | -0.01 | 0.02 | -0.05 |
| IMP49 | 0.01 | 0.11 | 0.00 | 0.04 | -0.07 | -0.10 | 0.12 | 0.02 | 0.04 | 0.21 | 0.35 | 0.00 | 0.12 | -0.02 | 0.08 | -0.05 | 0.00 | 0.12 |
| MISC52 | -0.06 | 0.01 | -0.08 | 0.15 | 0.02 | -0.05 | 0.01 | -0.05 | 0.10 | 0.01 | 0.01 | 0.00 | 0.02 | 0.05 | 0.70 | 0.09 | 0.14 | -0.07 |
| MISC53 | 0.07 | -0.01 | 0.00 | -0.09 | 0.03 | 0.06 | -0.01 | 0.06 | -0.04 | 0.06 | 0.07 | -0.06 | 0.01 | 0.04 | 0.74 | -0.01 | -0.13 | 0.07 |
| MISC54 | -0.03 | 0.11 | -0.02 | -0.01 | 0.64 | -0.02 | 0.05 | -0.02 | 0.02 | 0.03 | 0.02 | -0.10 | 0.10 | 0.03 | 0.04 | 0.05 | 0.10 | 0.00 |
| MISC55 | -0.02 | -0.04 | 0.04 | 0.00 | 0.84 | 0.04 | 0.00 | 0.04 | 0.01 | 0.03 | -0.10 | 0.02 | 0.00 | -0.04 | -0.03 | -0.01 | 0.06 | 0.11 |
| MISC56 | -0.03 | 0.02 | -0.06 | -0.01 | 0.83 | -0.02 | -0.01 | -0.02 | 0.03 | -0.02 | 0.08 | 0.04 | -0.02 | 0.01 | 0.04 | -0.03 | -0.11 | -0.04 |
| MISC59 | 0.06 | 0.10 | 0.03 | -0.10 | 0.01 | 0.28 | -0.05 | 0.10 | -0.07 | -0.06 | 0.41 | 0.35 | 0.02 | 0.02 | 0.04 | -0.03 | -0.01 | 0.03 |
| MISC60 | -0.03 | -0.03 | -0.01 | -0.04 | 0.04 | -0.03 | 0.02 | -0.10 | 0.03 | 0.05 | 0.04 | 0.75 | 0.06 | 0.09 | -0.01 | 0.05 | 0.00 | 0.02 |
| MISC61 | 0.03 | 0.01 | 0.10 | 0.04 | -0.04 | 0.07 | 0.07 | 0.06 | -0.06 | -0.02 | 0.02 | 0.74 | -0.04 | -0.02 | -0.06 | 0.01 | 0.00 | 0.02 |
| MISC62 | -0.03 | 0.18 | -0.04 | -0.05 | -0.03 | 0.04 | 0.00 | 0.16 | 0.18 | 0.03 | -0.01 | 0.10 | 0.00 | 0.57 | 0.04 | 0.01 | -0.05 | -0.02 |
| MISC63 | -0.02 | 0.12 | -0.02 | 0.02 | 0.01 | 0.00 | 0.13 | -0.06 | -0.03 | -0.02 | 0.04 | 0.06 | 0.06 | 0.65 | 0.12 | -0.07 | 0.12 | 0.01 |
| MISC64 | -0.08 | 0.79 | 0.01 | 0.05 | 0.04 | 0.02 | -0.02 | 0.01 | 0.01 | -0.01 | -0.07 | 0.02 | 0.03 | 0.03 | 0.03 | 0.03 | -0.07 | 0.05 |
| MISC65 | -0.07 | 0.66 | -0.02 | 0.02 | -0.01 | 0.02 | -0.02 | 0.06 | 0.05 | 0.06 | 0.01 | -0.01 | 0.05 | 0.12 | 0.06 | 0.01 | -0.02 | 0.07 |
| MISC66 | 0.18 | 0.53 | -0.04 | -0.01 | 0.18 | 0.07 | -0.04 | -0.07 | -0.01 | 0.05 | 0.12 | -0.07 | 0.00 | 0.12 | -0.03 | 0.04 | 0.10 | -0.09 |
| MISC67 | 0.08 | 0.55 | -0.13 | 0.07 | 0.14 | 0.03 | -0.04 | 0.01 | 0.06 | -0.03 | 0.13 | 0.04 | -0.02 | 0.01 | -0.05 | 0.09 | 0.21 | -0.17 |
| MISC69 | 0.05 | 0.06 | -0.05 | 0.01 | 0.14 | 0.03 | 0.03 | 0.00 | 0.05 | -0.06 | 0.03 | 0.06 | -0.02 | -0.02 | 0.01 | 0.05 | 0.02 | 0.66 |
| largest | maximum | itemNames | itemDescriptions | |
|---|---|---|---|---|
| 40 | PA1 | 0.79 | MISC64 | When working, is easily distracted or preoccupied by odors/engages in persistent sniffing of ground or objects |
| 41 | PA1 | 0.66 | MISC65 | Has difficulty shifting attention away from interesting or distracting stimuli (e.g., other dogs, odor, people, small animals, etc.) |
| 42 | PA1 | 0.53 | MISC66 | Is distracted or nervous in new, unfamiliar environments, has difficulty maintaining focus on work |
| 43 | PA1 | 0.55 | MISC67 | Is slow to recover after being distracted, startled, or frightened/takes a long time to resume work |
| 56 | PA1 | 0.59 | TRAIN07 | Unfocused; is easily distracted by interesting sights, sounds or smells |
| 30 | PA10 | 0.70 | MISC52 | Begs persistently for food when people are eating |
| 31 | PA10 | 0.74 | MISC53 | Steals food |
| 24 | PA11 | 0.84 | FEAR29 | When having nails trimmed, or feet touched/handled |
| 25 | PA11 | 0.66 | FEAR30 | When groomed or bathed |
| 17 | PA12 | 0.55 | FEAR22 | In response to sudden or loud noises (e.g., gun fire, car backfire, road drills, objects being dropped, etc.) |
| 20 | PA12 | 0.49 | FEAR25 | In response to strange or unfamiliar objects on or near sidewalks or walkways (e.g., plastic trash bags, leaves, litter, flags flapping, etc. |
| 36 | PA13 | 0.75 | MISC60 | Playful, puppyish, boisterous |
| 37 | PA13 | 0.74 | MISC61 | Active, energetic, always on the go |
| 9 | PA14 | 0.74 | ATT39 | Displays a strong attachment for you or another familiar person |
| 10 | PA14 | 0.49 | ATT40 | Unwilling to leave your side, even when working, reluctant to work at a distance from you/the handler |
| 11 | PA14 | 0.40 | ATT41 | Tends to nudge or paw you (or others) for attention |
| 27 | PA15 | 0.61 | IMP47 | Impulsive; doesn’t seem to think before s/he acts |
| 28 | PA15 | 0.67 | IMP48 | Becomes frustrated/impatient in a wide range of situations |
| 29 | PA15 | 0.35 | IMP49 | Is difficult to interrupt or distract when doing things s/he wants to do |
| 35 | PA15 | 0.41 | MISC59 | Hyperactive, restless, has trouble settling down |
| 44 | PA16 | 0.66 | MISC69 | Chases/follows shadows, light spots, etc. |
| 38 | PA17 | 0.57 | MISC62 | Becomes highly excited and/or distracted when encountering unfamiliar dogs |
| 39 | PA17 | 0.65 | MISC63 | Becomes highly excited and/or distracted when encountering unfamiliar people |
| 16 | PA18 | 0.82 | FEAR21 | When an unfamiliar person approaches the dog when s/he is away from his/her normal home environment or kennel |
| 18 | PA18 | 0.76 | FEAR23 | When an unfamiliar person visits your home or approaches the dog when in his/her home kennel |
| 19 | PA18 | 0.90 | FEAR24 | When an unfamiliar person tries to touch or pet the dog |
| 21 | PA18 | 0.39 | FEAR26 | When examined/treated by a veterinarian |
| 23 | PA18 | 0.39 | FEAR28 | When first exposed to unfamiliar situations (e.g., novel environments, first visit to the veterinarian, etc.) |
| 45 | PA2 | 0.50 | PLAY43 | Eagerly engages in play with new/unfamiliar people |
| 46 | PA2 | 0.88 | PLAY44 | Highly toy focused; attention riveted on tug toy/balls when these are held by handler or other person |
| 47 | PA2 | 0.86 | PLAY45 | Eagerly initiates play sessions; brings objects/toys to you/the handler and retrieves them when thrown |
| 48 | PA2 | 0.79 | PLAY46 | Hunts persistently for thrown or hidden toys/objects, not easily distracted from this task |
| 1 | PA3 | 0.61 | AGG09 | Barks, growls, attempts to bite when approached directly by an unfamiliar person while being walked/exercised on a leash |
| 2 | PA3 | 0.83 | AGG10 | Barks, etc. when unfamiliar persons approach the dog when s/he is in his/her kennel |
| 3 | PA3 | 0.73 | AGG14 | When strangers walk past when the dog is in his/her home run or kennel |
| 4 | PA3 | 0.60 | AGG15 | When an unfamiliar person tries to touch or pet the dog |
| 5 | PA4 | 0.53 | AGG16 | When approached directly by an unfamiliar dog while being walked/exercised on a leash |
| 6 | PA4 | 0.56 | AGG18 | When barked, growled, or lunged at by another dog |
| 7 | PA4 | 0.84 | AGG19 | Towards other familiar dogs |
| 8 | PA4 | 0.71 | AGG20 | When approached while playing with/chewing a favorite toy, bone, object, etc. by another familiar dog |
| 49 | PA5 | 0.82 | SEPR32 | Restlessness/agitation/pacing when left alone |
| 50 | PA5 | 0.78 | SEPR33 | Barking or whining when left alone |
| 51 | PA5 | 0.77 | SEPR34 | Chewing/scratching at doors, floor, fencing, etc., when left alone |
| 12 | PA6 | 0.55 | EXCITE35 | Excitable when you first arrive home, or at the dog’s kennel, after a brief absence |
| 13 | PA6 | 0.62 | EXCITE36 | Excitable when playing with you or other familiar persons |
| 14 | PA6 | 0.82 | EXCITE37 | Excitable just before being taken out for a walk |
| 15 | PA6 | 0.78 | EXCITE38 | Excitable just before being taken out for work or training |
| 32 | PA7 | 0.64 | MISC54 | Reluctant to/nervous about crossing grates or other unfamiliar surfaces |
| 33 | PA7 | 0.84 | MISC55 | Reluctant to/nervous about crossing shiny or slippery floors |
| 34 | PA7 | 0.83 | MISC56 | Nervous or frightened when ascending or descending some types of stairs |
| 52 | PA8 | 0.46 | TRAIN01 | Is hard to recall when off the leash |
| 53 | PA8 | 0.62 | TRAIN02 | Is slow to obey a ‘sit’ command |
| 54 | PA8 | 0.74 | TRAIN03 | Is slow to obey a ‘stay’ command |
| 55 | PA8 | 0.47 | TRAIN04 | Has difficulty attending/listening to things you say or do |
| 22 | PA9 | 0.84 | FEAR27 | When approached directly by an unfamiliar dog |
| 26 | PA9 | 0.80 | FEAR31 | When barked, growled, or lunged at by an unfamiliar dog |
| PA18 | PA1 | PA2 | PA3 | PA7 | PA5 | PA6 | PA4 | PA9 | PA8 | PA15 | PA13 | PA11 | PA17 | PA10 | PA14 | PA12 | PA16 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| alpha | 0.797 | 0.805 | 0.812 | 0.76 | 0.718 | 0.735 | 0.787 | 0.752 | 0.803 | 0.693 | 0.692 | 0.71 | 0.616 | 0.64 | 0.622 | 0.494 | 0.447 | 1 |
omega is thought to be better measure of reliability than alpha, because it looks at the relationships between all the items rather than just the ones within each factor. It’s different than alpha because it assumes that there is a genral factor, g, that all items have in common. This is listed as the first row of the table below.
There are three omegas for each factor:
From EFAtools::OMEGA documentation:
Omegas refer to the correlation between a factor and a unit-weighted composite score and thus the true score variance in a unit-weighted composite based on the respective indicators. Omega total is the total true score variance in a composite. Omega hierarchical is the true score variance in a composite that is attributable to the general factor, and omega subscale is the true score variance in a composite attributable to all subscales / group factors (for the whole scale) or to the specific subscale / group factor (for subscale composites).
Interpretation of omega_subscale
no universal guideline
0.50 is minimum, 0.75 preferable (watkins books,rodrigues16, zimbarg2005
## Omega total, omega hierarchical, omega subscale, H index, explained common variance (ECV), and percent of uncontaminated correlations (PUC) for the general factor (top row) and omegas and H index for the group factors:
##
## tot hier sub H ECV PUC
## g 0.952 0.607 0.165 0.896 0.236 0.954
## F1 0.816 0.398 0.418 0.674
## F2 0.724 0.076 0.648 0.670
## F3 0.751 0.207 0.544 0.629
## F4 0.588 0.258 0.330 0.400
## F5 0.686 0.001 0.685 0.712
## F6 0.618 0.090 0.528 0.612
## F7 0.567 0.188 0.380 0.569
## F8 0.498 0.082 0.416 0.416
## F9 0.630 0.254 0.376 0.454
## F10 0.806 0.293 0.513 0.819
## F11 0.827 0.067 0.760 0.874
## F12 0.743 0.117 0.626 0.795
## F13 0.741 0.155 0.586 0.770
## F14 0.842 0.155 0.687 0.768
## F15 0.748 0.024 0.724 0.816
## F16 0.841 0.214 0.627 0.748
## F17 0.662 0.180 0.482 0.648
## F18 0.843 0.231 0.612 0.708
| fits12 | fits13 | fits14 | fits15 | fits16 | fits17 | fits18 | |
|---|---|---|---|---|---|---|---|
| Bartlett test chi-square | 32708.77 | 35060 | 34280.193 | 35265.38 | 37685.24 | 39253.54 | 38936 |
| Bartlett test degrees of freedom | 1035.00 | 1128 | 1128.000 | 1275.00 | 1431.00 | 1540.00 | 1540 |
| Bartlett test p-value | 0.00 | 0 | 0.000 | 0.00 | 0.00 | 0.00 | 0 |
| KMO | 0.85 | 1 | 0.849 | 0.85 | 0.85 | 0.85 | 1 |
| Tucker-Lewis Index | 0.76 | 1 | 0.760 | 0.75 | 0.72 | 0.72 | 1 |
| Chi-square | 4483.85 | 5318 | 4373.565 | 4709.92 | 5426.57 | 5699.96 | 5065 |
| Degrees of freedom for chi-square | 549.00 | 582 | 547.000 | 615.00 | 687.00 | 724.00 | 685 |
| P-value for chi-square | 0.00 | 0 | 0.000 | 0.00 | 0.00 | 0.00 | 0 |